Administrative Services Agreement, dated November 23, 2021, between the Company, Opco, Beard Energy Transition Acquisition Holdings Sub LLC and the Sponsor

Exhibit 10.4

BEARD ENERGY TRANSITION ACQUISITION HOLDINGS LLC

595 Madison Avenue, 29th Floor

New York, NY 10022

November 23, 2021

Beard Energy Transition Acquisition Holdings Sub LLC

595 Madison Avenue, 29th Floor

New York, NY 10022

Re:Administrative Support Agreement

Gentlemen:

This letter agreement by and between Beard Energy Transition Acquisition Corp. (the “SPAC”), Beard Energy Transition Acquisition Holdings LLC (the “Company”), Beard Energy Transition Acquisition Sponsor LLC (“Sponsor”), and Beard Energy Transition Acquisition Holdings Sub LLC (“Affiliate”), an affiliate of Sponsor will confirm our agreement that, commencing on the date certain securities of the SPAC are first listed on the New York Stock Exchange (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the SPAC of an initial business combination or the SPAC’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

(i)       Affiliate shall provide to the Company administrative support as may be reasonably required by the Company. As reimbursement therefor, beginning on the Listing Date and continuing monthly thereafter until the Termination Date, the Company shall pay Affiliate (and Affiliate will receive on behalf of itself or, to the extent it causes another person to make support available to Company, as nominee on behalf of such other person) the sum of $25,000 per month.  Such payment may be made to Affiliate or to such recipients providing such support to the Company, as designated by the SPAC or the Company. Of such monthly reimbursement, it is contemplated that (i) $16,667 per month will be paid to Sarah James, as Chief Financial Officer of the Company, and (ii) $8,333 per month will be paid to another consultant to the Company, in each case so long as such individual provides services to the Company or Beard Energy Transition Acquisition Corp.  Although the sums payable hereunder are fixed, the parties intend that such sums constitute solely a reimbursement for the costs described herein without any mark-up or other profits and agree that that such fixed sums constitute a reasonable estimate of such costs.

(ii)       Affiliate hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of, or arising out of, this letter agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public shareholders of the Company and into which substantially all of the proceeds of the Company’s initial public offering and a portion of the

proceeds from the sale of the private placement warrants will be deposited (the “Trust Account”), and hereby irrevocably waives any Claim it may have in the future, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.

(iii)       To the fullest extent permitted by applicable law, the Company hereby agrees to defend, indemnify, hold harmless and exonerate (including the advancement of expenses to the fullest extent permitted by applicable law) Sponsor, Affiliate and their respective affiliates (each, a “Sponsor Indemnitee”) from any and all costs, fees, expenses, judgments, liabilities, fines, penalties, reasonable attorneys’ fees and amounts paid in settlement (including all interest, assessments and other charges paid or payable in connection with or in respect of such costs, fees, expenses, judgments, liabilities, fines, penalties and amounts paid in settlement) actually, and reasonably, incurred by a Sponsor Indemnitee or on a Sponsor Indemnitee’s behalf in connection with any threatened, pending or completed action, suit, arbitration, mediation, alternate dispute resolution mechanism, investigation, inquiry, hearing or any other actual, threatened or completed proceeding instituted by the Company or any third party, whether civil, criminal, administrative or investigative in nature, in respect of any investment opportunities sourced by a Sponsor Indemnitee for the Company or any liability arising with respect to a Sponsor Indemnitee’s activities in connection with the affairs of the Company (in each case to the extent that such indemnification, hold harmless and exoneration obligations with respect to such matters are not expressly covered by a separate written agreement between the Company or the SPAC, on the one hand, and the applicable Sponsor Indemnitee, on the other hand); provided, that in no event shall a Sponsor Indemnitee be entitled to be indemnified or held harmless hereunder in respect of any costs, fees, expenses, judgments, liabilities, fines, penalties and amounts paid in settlement (if any) that Sponsor Indemnitee may incur by reason of such person’s own actual fraud or intentional misconduct; provided further, for the avoidance of doubt, that under no circumstance shall a Sponsor Indemnitee have a Claim to any monies or assets held in the Trust Account, and the Company shall not be permitted to procure monies or assets held in the Trust Account for the satisfaction of its obligations to any Sponsor Indemnitee in respect of the indemnification provided hereunder.  The Sponsor Indemnitees shall be third party beneficiaries of this paragraph.

This letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

This letter agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.

No party hereto may assign either this letter agreement or any of its rights, interests or obligations hereunder without the prior written approval of the other parties; provided, however, that Affiliate may assign this letter agreement, in whole or in part, to Sponsor or any other person that directly, or indirectly through one or more intermediaries, controls, or is controlled by, or is

2

under common control with, Sponsor without the prior written approval of the other parties. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

This letter agreement constitutes the entire relationship of the parties hereto with respect to the matters contemplated herein, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) with respect to this letter agreement shall be governed by, construed in accordance with and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles.

[Signature Page Follows]

3

Signature Page to Administrative Support Agreement