Exhibit 10.4


 


M3-Brigade Acquisition III Corp.


1700 Broadway, 19th Floor


New York, NY 10019


 


November 1, 2022


 


Mr. Alan J. Carr


[***]


[***]


[***]


 


Dear Mr. Carr:


 


On behalf of the board of directors (the “Board”)
of M3-Brigade Acquisition III Corp. (the “Company”), I am pleased to invite you to become a member of the Board.


 


The Board intends that you will serve as an independent
director, as such term has been construed under Delaware law and pursuant to the applicable standards of the New York Stock Exchange,
the Sarbanes-Oxley Act of 2002 and the Company’s Corporate Governance Guidelines. By signing this engagement agreement, you confirm
that:


 


		(a)	you do not possess material business, close personal relationships, or other affiliations, or any history
of any such material business, close personal relationships, or other affiliations, with the Company or any of its major debtholders or
equityholders that would cause you to be unable to (i) exercise independent judgment based on the best interests of the Company or (ii)
make decisions and carry out your responsibilities as a member of the Board, in each case, in accordance with the terms of the Company’s
certificate of incorporation and bylaws, as well as applicable law;



 


		(b)	you do not directly or indirectly (i) own securities that would cause your interests to differ in any
material respect from the interests of the Company’s public stockholders or (ii) otherwise have reason to obtain a benefit from
the consummation of the Company’s initial business combination that is not similarly available to such public stockholders are a
result of such initial business combination; and



 


		(c)	you will use commercially reasonable efforts to maintain your independence during your tenure as a director.



 


As a member of the Board, you will receive cash
compensation in the amount of $125,000 for your service as an independent director. Such fee will not be adjusted to reflect the duration
of your tenure as an independent director. In addition, you will be reimbursed for all reasonable and documented out-of-pocket expenses
incurred by you in connection with your service to the Company as a member of the Board. You understand that the Company may seek to appoint
you to one or more Board committees or special committees relating to the evaluation, negotiation and consummation of the Company’s
initial business combination and, in such event, if you agree to serve as a member of any such committee, you will not receive further
compensation. You also will be covered by the Company’s indemnification obligations to directors and by its directors’ and
officers’ liability insurance policy, as the same may be amended from time to time with the consent of the Board.


 






     


     


    

 


Our expectation is that the Board will meet at
least quarterly, but will likely meet more frequently when considering a potential initial business combination.
We ask that you make yourself available to participate in those meetings either in person or telephonically as may be appropriate.
We also ask that you make yourself available to participate in various telephonic meetings with the Company’s directors, officers,
and/or advisors from time to time. These meetings will not be separately compensable time.


 


Your service on the Board will be in accordance
with, and subject to, the organizational documents of the Company and applicable law concerning the service of directors in the state
of Delaware, as the same may be further amended from time to time. In accepting this offer, you are representing to us that you do not
know of any conflict or legal prohibition that would restrict you from becoming, or could reasonably be expected to preclude you from
remaining, a member of the Board, including Section 8 of the Clayton Act and other similar provisions.


 


You and the Company acknowledge that this engagement
agreement is governed by, and construed and interpreted in accordance with, the laws of the State of Delaware, without giving effect to
any choice or conflict of law provision or rule (whether of the state of Delaware or any other jurisdiction) that would cause the application
of the laws of any jurisdictions other than the state of Delaware.


 


This engagement agreement sets forth the terms
of your service with the Company and supersedes any prior representations or agreements, whether written or oral. This engagement agreement
must be accepted within five business days of the date set forth above, and it may not be modified or amended except by a written agreement,
signed by a duly authorized representative of the Company and by you.


 


We look forward to working with you.


 


	 	Very truly yours,
	 	 
	 	M3-BRIGADE ACQUISITION III CORP.
	 	 
	 	/s/ Mohsin Y. Meghji
	 	Mohsin Y. Meghji
	 	Executive Chairman



 


ACCEPTED AND AGREED:


 


I hereby accept, and consent to be designated as a member of the Board
and agree to so serve, subject to the terms and conditions set forth herein.


 


	/s/
    Alan J. Carr	 	Date: November 1, 2022
	Alan J. Carr