Filed Pursuant to Rule 424(b)(3)
Registration No. 333-270624

SUPPLEMENT NO. 5 TO

PROSPECTUS OF HAMMERHEAD ENERGY INC.

This prospectus supplement amends and supplements the prospectus dated May 1, 2023 as supplemented or amended from time to time (the "Prospectus"), which forms a part of our Registration Statement on Form F-1 (Registration Statement No. 333-270624). This prospectus supplement is being filed to update and supplement the information included or incorporated by reference in the Prospectus with the information contained in our Report on Form 6-K, which was furnished to the Securities and Exchange Commission on August 16, 2023 (the "Form 6-K"). Accordingly, we have attached the Form 6-K to this prospectus supplement.

This prospectus supplement updates and supplements the information in the Prospectus and is not complete without, and may not be delivered or utilized except in combination with, the Prospectus, including any amendments or supplements thereto. This prospectus supplement should be read in conjunction with the Prospectus and if there is any inconsistency between the information in the Prospectus and this prospectus supplement, you should rely on the information in this prospectus supplement.

Our Class A Common Shares and Warrants are listed on The Nasdaq Stock Market LLC ("Nasdaq") under the symbols "HHRS" and "HHRSW", respectively, and on the Toronto Stock Exchange (the "TSX") under the symbols "HHRS" and "HHRS.WT," respectively. On August 15, 2023, the last reported sales prices of the Class A Common Shares on Nasdaq and the TSX were $10.36 and C$13.75 respectively, and the last reported sales prices of the Warrants were $2.13 and C$2.81, respectively.

Investing in our securities involves a high degree of risk. You should review carefully the risks and uncertainties described under the heading "Risk Factors" beginning on page 5 of the Annual Report and beginning on page 5 of the Prospectus, and under similar headings in any amendment or supplements to the Prospectus.

Neither the U.S. Securities and Exchange Commission nor any state securities regulatory agency has approved or disapproved of the securities offered by this prospectus supplement or the Prospectus or determined if the Prospectus or this prospectus supplement is truthful or complete. Any representation to the contrary is a criminal offense.

This Supplement No. 5 is dated August 16, 2023.

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13A-16 OR 15D-16

UNDER THE SECURITIES EXCHANGE ACT OF 1934

For the month of August, 2023

Commission File Number 001-41630

HAMMERHEAD ENERGY INC.

(Exact name of Registrant as specified in its charter)

N/A

(Translation of Registrant's name)

Suite 2700, 525-8th Avenue SW

Calgary, Alberta, T2P 1G1

(403) 930-0560

(Address and telephone number of registrant's principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F:

Form 20-F ☒ Form 40-F ☐

DOCUMENTS INCLUDED AS PART OF THIS REPORT

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Eighth Avenue Place  |  Suite 2700, 525 - 8 Ave SW  |  Calgary, Alberta  T2P 1G1

CALGARY, ALBERTA - August 16, 2023 -  Hammerhead Energy Inc. ("Hammerhead" or the "Company") (NASDAQ: HHRS, HHRSW; TSX: HHRS, HHRS.WT) today announced that it will redeem for cash all of its outstanding public warrants to purchase its Class A Common Shares ("Common Shares"), originally issued as part of the units sold in Decarbonization Plus Acquisition Corporation IV's ("DCRD") initial public offering (the "Public Warrants") and originally issued pursuant to the Warrant Agreement, dated August 10, 2021 (the "Warrant Agreement"), by and between DCRD and Continental Stock Transfer & Trust Company, as warrant agent, and assumed by the Company pursuant to an amended and restated warrant agreement, dated February 22, 2023 (the "A&R Warrant Agreement"), by and among the Company, Computershare Inc. and Computershare Trust Company, N.A., as warrant agent (the "Warrant Agent"), for a redemption price of US$0.10 per Public Warrant (the "Redemption Price").

Under the terms of the Warrant Agreement, the Company is entitled to redeem all of its outstanding Public Warrants for cash if the last sales price of the Common Shares reported equals or exceeds US$10.00 per share on the trading day prior to the date of the notice of redemption (the "Notice of Redemption"). This share price performance requirement was satisfied as of August 15, 2023.

At the Company's request, the Warrant Agent has delivered the Notice of Redemption to each of the registered holders of the Public Warrants on behalf of the Company.

The Public Warrants may be exercised by the registered holders thereof until 5 p.m. New York City time on September 15, 2023 (the "Redemption Date") to purchase Common Shares underlying such warrants, (i) in cash, at the exercise price of US$11.50 per share or (ii) on a "cashless basis" in which the exercising holder will receive a number of Common Shares to be determined in accordance with the terms of the A&R Warrant Agreement and based on the Redemption Date and the average last reported sale price (the "Fair Market Value") of the Common Shares during the 10 trading days immediately following the date on which the Notice of Redemption is sent to holders of Public Warrants. The Company will inform holders of the Fair Market Value no later than one business day after such 10‐trading day period ends. In no event will the number of Common Shares issued in connection with an exercise on a cashless basis exceed 0.361 Common Shares per Public Warrant. If any holder of Public Warrants would, after taking into account all of such holder's Public Warrants exercised at one time, be entitled to receive a fractional interest in a Common Share, the number of shares the holder will be entitled to receive will be rounded down to the nearest whole number of shares. Holders of Public Warrants must follow the instructions provided in the Notice of Redemption in order to validly exercise their Public Warrants.

Public Warrants that remain unexercised following 5 p.m. New York City time on September 15, 2023 will be void and no longer exercisable, and the registered holders of such unexercised Public Warrants will only be entitled to receive the Redemption Price per Public Warrant. Additionally, at 5 p.m. New York City time on the Redemption Date, the Public Warrants will cease trading on the NASDAQ Stock Market and the Toronto Stock Exchange.

The Common Shares underlying the Public Warrants have been registered by the Company under the Securities Act of 1933, as amended, and are covered by a registration statement filed on Form F-1 with, and declared effective by, the Securities and Exchange Commission (the "SEC") (Registration No. 333-270624).

Eighth Avenue Place  |  Suite 2700, 525 - 8 Ave SW  |  Calgary, Alberta  T2P 1G1

Questions concerning redemption and exercise of such Public Warrants can be directed to Computershare, Inc., Attn: Corporate Actions, 150 Royall Street, Canton, MA 02021, or by telephone: 1-800-736-3001.

For a copy of the Notice of Redemption, please visit our investor relations website at ir.hhres.com. A copy of the Notice of Redemption has also been filed on the Company's EDGAR profile with the SEC at www.sec.gov.

This press release shall not constitute an offer to sell or the solicitation of an offer to buy any of the Company's securities and shall not constitute an offer, solicitation or sale in any jurisdiction in which such offering, solicitation or sale would be unlawful.

About Hammerhead Energy

Hammerhead is a Calgary, Canada-based energy company, with assets and operations in Alberta targeting the Montney formation. Hammerhead Resources Inc., the predecessor entity to Hammerhead Resources ULC, a wholly owned subsidiary of Hammerhead, was formed in 2009.

Forward-Looking Statements

This press release includes certain statements that may constitute "forward-looking statements" within the meaning of applicable Canadian and U.S. securities laws, including Section 27A of the Securities Act of 1933, as amended, and Section 21E of the Securities Exchange Act of 1934, as amended. Forward-looking statements include, but are not limited to, statements that refer to projections, forecasts or other characterizations of future events or circumstances, including any underlying assumptions. The words "anticipate," "believe," "continue," "could," "estimate," "expect," "intends," "may," "might," "plan," "possible," "potential," "predict," "project," "should," "would" and similar expressions may identify forward-looking statements, but the absence of these words does not mean that a statement is not forward-looking. Forward-looking statements may include, for example, statements about the Company's ability to complete the redemption on anticipated terms and timelines or at all. These forward-looking statements speak only as of the date of this press release and are based on information available as of the date of this press release and current expectations, forecasts and assumptions, and involve a number of judgments, risks and uncertainties. Accordingly, forward-looking statements should not be relied upon as representing the Company's views as of any subsequent date, and the Company does not undertake any obligation to update forward-looking statements to reflect events or circumstances after the date they were made, whether as a result of new information, future events or otherwise, except as may be required under applicable securities laws. You should not place undue reliance on these forward-looking statements. As a result of a number of known and unknown risks and uncertainties, the Company's actual results or performance may be materially different from those expressed or implied by these forward-looking statements. Some factors that could cause actual results to differ include the risks and uncertainties indicated from time to time in the Company's filings with the Alberta Securities Commission and the SEC, including those under "Risk Factors" therein.

Eighth Avenue Place  |  Suite 2700, 525 - 8 Ave SW  |  Calgary, Alberta  T2P 1G1

Contacts

For further information, please contact:

Scott Sobie

President and CEO

Hammerhead Energy Inc.

403-930-0560

Mike Kohut

Senior Vice President and CFO

Hammerhead Energy Inc.

403-930-0560

Kurt Molnar

Vice President Capital Markets & Corporate Planning

Hammerhead Energy Inc.

403-930-0560

August 16, 2023

NOTICE OF REDEMPTION OF CERTAIN WARRANTS (CUSIP 408302115)

Dear Public Warrant Holder,

Hammerhead Energy Inc. (the "Company") hereby gives notice that it is redeeming, at 5:00 p.m. New York City time on September 15, 2023 (the "Redemption Date"), all of the Company's outstanding public warrants (the "Public Warrants") to purchase the Company's Class A Common Shares, without par value (the "Common Shares"), that were originally issued under the Warrant Agreement, dated August 10, 2021 (the "Warrant Agreement"), by and between Decarbonization Plus Acquisition Corporation IV ("DCRD") and Continental Stock Transfer & Trust Company, as warrant agent, as part of the units sold in DCRD's initial public offering (the "IPO"), and assumed by the Company pursuant to an amended and restated warrant agreement, dated February 22, 2023 (the "A&R Warrant Agreement"), by and among the Company, Computershare Inc. and Computershare Trust Company, N.A., as warrant agent (the "Warrant Agent"), for a redemption price of $0.10 per Public Warrant (the "Redemption Price"). Each Public Warrant entitles the holder thereof to purchase one Common Share for a purchase price of $11.50 per share, subject to certain adjustments. Any Public Warrants that remain unexercised at 5:00 p.m. New York City time on the Redemption Date will be void and no longer exercisable and their holders will have no rights with respect to those Public Warrants, except to receive the Redemption Price or as otherwise described in this notice for holders who hold their Public Warrants in "street name." The Public Warrants trade on the NASDAQ Stock Market ("NASDAQ") and the Toronto Stock Exchange ("TSX") under the symbols "HHRSW" and "HHRS.WT", respectively. On August 15, 2023, the closing prices of the Common Shares on the NASDAQ and the TSX were $10.36 and C$13.75, respectively.

Additionally, at 5:00 p.m. New York City time on the Redemption Date, the Public Warrants will cease trading on the NASDAQ and the TSX.

TERMS OF REDEMPTION; CESSATION OF RIGHTS

The rights of the Public Warrant holders to exercise their Public Warrants will terminate immediately prior to 5:00 p.m. New York City time on the Redemption Date. At 5:00 p.m. New York City time on the Redemption Date and thereafter, holders of unexercised Public Warrants will have no rights with respect to those warrants, except to receive the Redemption Price or as otherwise described in this notice for holders who hold their Public Warrants in "street name." We encourage you to consult with your broker, financial advisor and/or tax advisor to consider whether or not to exercise your Public Warrants. Please note that the act of exercising is VOLUNTARY, meaning that a holder of Public Warrants must instruct its broker to submit its Public Warrants for exercise.

The Company is exercising this right to redeem the Public Warrants pursuant to Section 6 of the A&R Warrant Agreement. Pursuant to Section 6.2 of the A&R Warrant Agreement, the Company has the right to redeem all of the outstanding Public Warrants if the last reported sales price of the Common Shares equals or exceeds $10.00 per share on the trading day prior to the date on which a notice of redemption is given. This share price performance requirement was satisfied as of August 15, 2023.

EXERCISE PROCEDURE

Public Warrant holders have until 5:00 p.m. New York City time on the Redemption Date to exercise their Public Warrants to purchase Common Shares. Public Warrants may be exercised (i) for cash, at a cash price of $11.50 per Public Warrant exercised (the "Cash Exercise Price") or (ii) on a "cashless basis" in which the exercising holder will receive a number of Common Shares to be determined in accordance with the terms of the A&R Warrant Agreement and based on the Redemption Date and the average last reported sale price (the "Fair Market Value") of the Common Shares during the 10 trading days immediately following the date on which this notice of redemption is sent to holders of Public Warrants. The Company will provide holders the Fair Market Value no later than one business day after such 10-trading day period ends. In no event will the number of Common Shares issued in connection with an exercise on a cashless basis exceed 0.361 Common Shares per Public Warrant. If any holder of Public Warrants would, after taking into account all of such holder's Public Warrants exercised at one time, be entitled to receive a fractional interest in a Common Share, the number of shares the holder will be entitled to receive will be rounded down to the nearest whole number of shares.

Payment of the Cash Exercise Price may be made by wire transfer of immediately available funds. Wire instructions will be provided to the Depository Trust Company and will otherwise be provided upon request.

Those who hold their Public Warrants in "street name" should immediately contact their broker to determine their broker's procedure for exercising their Public Warrants because the process to exercise is voluntary.

Persons who are holders of record of their Public Warrants may exercise their Public Warrants by sending (1) a fully and properly completed "Election to Purchase" (a form of which is attached hereto as Annex A), duly executed and indicating, among of things, the number of Public Warrants being exercised and whether such Public Warrants are being exercised on a cash or cashless basis, and (2) if exercised for cash, payment in full of the Cash Exercise Price via wire transfer or other method of payment permitted by the A&R Warrant Agreement to the Warrant Agent:

Computershare Trust Company, N.A.

150 Royall Street, Canton, MA 02021

Attention: Corporate Actions

Telephone: 1-800-736-3001

The method of delivery of the Public Warrants is at the option and risk of the holder, but if mail is used, registered mail properly insured is suggested.

The fully and properly completed Election to Purchase and, if the applicable Warrants are exercised for cash, payment in full of the Cash Exercise Price must be received by Computershare Trust Company, N.A. prior to 5:00 p.m. New York City time on the Redemption Date. Subject to the following paragraph, any failure to deliver a fully and properly completed Election to Purchase or, if the applicable Warrants are exercised for cash, the payment in full of the Cash Exercise Price before such time will result in such holder's Public Warrants being redeemed and not exercised.

WARRANTS HELD IN STREET NAME

For holders of Public Warrants who hold their warrants in "street name," provided that a Notice of Guaranteed Delivery and, in the case of a cash exercise, payment in full of the Cash Exercise Price, is received by the Warrant Agent prior to 5:00 p.m. New York City time on the Redemption Date, broker-dealers shall have two business days from the Redemption Date, or 5:00 p.m. New York City time on September 15, 2023, to deliver the Public Warrants to the Warrant Agent. Any such Public Warrant received without the Election to Purchase or the Notice of Guaranteed Delivery having been duly executed and fully and properly completed or, in the case of a cash exercise, without the payment in full of the Cash Exercise Price will be deemed to have been delivered for redemption (at $0.10 per Public Warrant), and not for exercise.

REDEMPTION PROCEDURE

Payment of the Redemption Price will be made by the Company upon presentation and surrender of a Public Warrant for payment after 5:00 p.m. New York City time on the Redemption Date. Those who hold their shares in "street name" should contact their broker to determine their broker's procedure for redeeming their Public Warrants.

*****

Any questions you may have about redemption and exercising your Public Warrants may be directed to the Warrant Agent at its address and telephone number set forth above.

[Signature page to the Notice of Redemption]

Annex A

HAMMERHEAD ENERGY INC.

Election to Purchase

(To Be Executed Upon Exercise of Warrant)

The undersigned hereby irrevocably elects to exercise the right, represented by this Warrant Certificate, to receive _________ Class A Common Shares and herewith tenders payment for such Class A Common Shares to the order of Hammerhead Energy Inc. (the "Company") in the amount of $_________ in accordance with the terms hereof. The undersigned requests that the register of members of the Company be updated to reflect the issuance of such Class A Common Shares and a certificate for such Class A Common Shares be registered in the name of _________, whose address is _________ and that such Class A Common Shares be delivered to _________ whose address is _________. If said number of Class A Common Shares is less than all of the Class A Common Shares purchasable hereunder, the undersigned requests that a new Warrant Certificate representing the remaining balance of such Class A Common Shares be registered in the name of _________, whose address is  _________ and that such Warrant Certificate be delivered to  _________, whose address is _________.

In the event that the Warrant has been called for redemption by the Company pursuant to Section 6.2 of the Warrant Agreement and the undersigned elects to exercise its Warrant pursuant to a Make-Whole Exercise, the number of Class A Common Shares that this Warrant is exercisable for shall be determined in accordance with Section 6.2 of the Warrant Agreement.

In the event that the Warrant is a Private Placement Warrant that is to be exercised on a "cashless" basis pursuant to subsection 3.3.1(c) of the Warrant Agreement, the number of Class A Common Shares that this Warrant is exercisable for shall be determined in accordance with subsection 3.3.1(c) of the Warrant Agreement.

In the event that the Warrant is to be exercised on a "cashless" basis pursuant to Section 7.4 of the Warrant Agreement, the number of Class A Common Shares that this Warrant is exercisable for shall be determined in accordance with Section 7.4 of the Warrant Agreement.

In the event that the Warrant may be exercised, to the extent allowed by the Warrant Agreement, through cashless exercise (i) the number of Class A Common Shares that this Warrant is exercisable for would be determined in accordance with the relevant section of the Warrant Agreement which allows for such cashless exercise; (ii) the holder hereof hereby undertakes to pay on demand the relevant aggregate nominal value for the Class A Common Shares to be issued, and (iii) the holder hereof shall complete the following: The undersigned hereby irrevocably elects to exercise the right, represented by this Warrant Certificate, through the cashless exercise provisions of the Warrant Agreement, to receive _________ Class A Common Shares. If said number of Class A Common Shares is less than all of the Class A Common Shares purchasable hereunder (after giving effect to the cashless exercise), the undersigned requests that a new Warrant Certificate representing the remaining balance of such Class A Common Shares be registered in the name of _________, whose address is _________ and that such Warrant Certificate be delivered to _________, whose address is _________.

[Signature Page Follows]

Date:

Signature Guaranteed:

THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM, PURSUANT TO SEC RULE 17Ad-15 (OR ANY SUCCESSOR RULE)) UNDER THE SECURITIES EXCHANGE ACT OF 1934, AS AMENDED.