Exhibit 4.1


 


	NUMBER	UNITS
	U-	 


 


SEE REVERSE FOR CERTAIN DEFINITIONS


 


CUSIP 88605T 209


 


THUNDER BRIDGE CAPITAL PARTNERS III INC.


 


UNITS CONSISTING OF ONE SHARE OF CLASS A
COMMON STOCK AND ONE-QUARTER OF ONE 

REDEEMABLE WARRANT,


 


EACH WHOLE WARRANT ENTITLING THE HOLDER
TO PURCHASE ONE SHARE OF CLASS A COMMON STOCK


 


THIS CERTIFIES THAT                     
is the owner of          Units.


 


Each Unit (“Unit”)
consists of one (1) share of Class A common stock, par value $0.0001 per share (“Common Stock”),
of Thunder Bridge Capital Partners III Inc., a Delaware corporation (the “Company”), and one-quarter
of one redeemable warrant (the “Warrant”). Each whole Warrant entitles the holder to purchase one
(1) share (subject to adjustment) of Common Stock for $11.50 per share (subject to adjustment). Each whole Warrant will
become exercisable on the later of (i) thirty (30) days after the Company’s completion of a merger, capital stock
exchange, asset acquisition, stock purchase, reorganization or other similar business combination with one or more businesses (each
a “Business Combination”), or (ii) twelve (12) months from the closing of the Company’s
initial public offering, and will expire unless exercised before 5:00 p.m., New York City Time, on the date that is five (5) years
after the date on which the Company completes its initial Business Combination, or earlier upon redemption or liquidation (the
“Expiration Date”). The Common Stock and Warrants comprising the Units represented by this certificate
are not transferable separately prior to            , 2021, unless Morgan
Stanley & Co. LLC elects to allow separate trading earlier, subject to the Company’s filing of a Current Report on Form 8-K
with the Securities and Exchange Commission containing an audited balance sheet reflecting the Company’s receipt of the gross
proceeds of the Company’s initial public offering and issuing a press release announcing when separate trading will begin. The
terms of the Warrants are governed by a Warrant Agreement, dated as of             
, 2021, between the Company and Continental Stock Transfer & Trust Company, as Warrant Agent, and are subject to the terms
and provisions contained therein, all of which terms and provisions the holder of this certificate consents to by acceptance hereof. Copies
of the Warrant Agreement are on file at the office of the Warrant Agent at 1 State Street, 30th Floor, New York,
New York 10004, and are available to any Warrant holder on written request and without cost.


 


This certificate is not valid unless countersigned
by the Transfer Agent and Registrar of the Company.


 


This certificate shall be governed by and
construed in accordance with the internal laws of the State of New York.


 


Witness the facsimile signature of a duly
authorized signatory of the Company.


 


	 	 	 
	Authorized Signatory	 	Transfer Agent


 






     


     


    

 


Thunder Bridge Capital Partners III Inc.


 


The Company will furnish without charge
to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating, optional
or other special rights of each class of stock or series thereof of the Company and the qualifications, limitations, or restrictions
of such preferences and/or rights.


 


The following abbreviations, when used
in the inscription on the face of this certificate, shall be construed as though they were written out in full according to applicable
laws or regulations: 


 


	TEN COM      —    as tenants in common	 	UNIF GIFT MIN ACT	 	—	 	 	 	Custodian	 	 
	TEN ENT       —    as tenants by the entireties	 	 	 	 	 	    (Cust)    	 	 	 	      (Minor)      
	 	 	 	 
	JT TEN           —     as joint tenants with right of survivorship and not as tenants in common	 	 	 	under Uniform Gifts to Minors Act
	 	 	 	 	 
	 	 	 	 	 	 	(State)


 


Additional abbreviations may also be used
though not in the above list.


 


For value received,                     
hereby sell, assign and transfer unto                     


 


(PLEASE INSERT SOCIAL SECURITY OR OTHER
IDENTIFYING NUMBER OF ASSIGNEE)


 


(PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING
ZIP CODE, OF ASSIGNEE)


 


Units represented by the within Certificate,
and do hereby irrevocably constitute and appoint


 


Attorney to transfer the said Units on the books of
the within named Company with full power of substitution in the premises.


 


Dated


 


	 	 
	 	 
	 	 
	 	Notice: The signature to this assignment must correspond with the name as written upon the face of the certificate in every particular, without alteration or enlargement or any change whatever.


 


	Signature(s) Guaranteed:	 
	 	 
	 	 
	 	 
	THE SIGNATURE(S) MUST 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 S.E.C. RULE 17Ad-15 (OR ANY SUCCESSOR RULE).	 


 


In each case, as more fully described
in the Company’s final prospectus dated                   ,
2021, the holder(s) of this certificate shall be entitled to receive a pro-rata portion of certain funds held in the trust
account established in connection with its initial public offering only in the event that (i) the Company redeems the shares
of Class A common stock sold in the Company’s initial public offering and liquidates because it does not consummate
an initial business combination within the time period set forth in the Company’s amended and restated certificate of incorporation,
as the same may be amended from time to time (such date being referred to herein as the “Last Date”), (ii) the
Company redeems the shares of Class A common stock sold in its initial public offering in connection with a stockholder vote
to amend the Company’s amended and restated certificate of incorporation to modify the substance or timing of the Company’s
obligation to allow redemption in connection with the Company’s initial business combination or to redeem 100% of the Class A
common stock if it does not consummate an initial business combination by the Last Date, or with respect to any other provision
relating to stockholders’ rights or pre-initial Business Combination activity, or (iii) if the holder(s) seek(s) to
redeem for cash his, her or its respective shares of Class A common stock in connection with a tender offer (or proxy solicitation,
solely in the event the Company seeks stockholder approval of the proposed initial business combination) setting forth the details
of a proposed initial business combination. In no other circumstances shall the holder(s) have any right or interest of any
kind in or to the trust account.