Exhibit 10.3





October
13, 2015


 


Capitol
Acquisition Corp. III


509 7th
Street, N.W.


Washington,
D.C. 20004


 


Citigroup
Global Markets Inc.


388
Greenwich Street


New
York, New York 10013


 


Deutsche
Bank Securities Inc.


60
Wall Street


New
York, New York 10005


 


Credit
Suisse Securities (USA) LLC


Eleven
Madison Avenue


New
York, New York 10010


 


	 	Re:	Initial Public Offering




 


Gentlemen:


 


This
letter is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”)
entered into by and between Capitol Acquisition Corp. III, a Delaware corporation (the “Company”), and
Citigroup Global Markets Inc., Deutsche Bank Securities Inc. and Credit Suisse Securities (USA) LLC as representatives (collectively
the “Representatives”) of the several Underwriters named in Schedule I thereto (the “Underwriters”),
relating to an underwritten initial public offering (the “IPO”) of the Company’s units (the “Units”),
each comprised of one share of the Company’s common stock, par value $0.0001 per share (the “Common Stock”),
and one half of one warrant, each whole warrant exercisable for one share of Common Stock (each, a “Warrant”).
Certain capitalized terms used herein are defined in paragraph 14 hereof.


 


In
order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the IPO, and in
recognition of the benefit that such IPO will confer upon the undersigned as a stockholder of the Company, and for other good
and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned hereby agrees with the
Company as follows:


 


1.             If
the Company solicits approval of its stockholders of a Business Combination,  the undersigned will vote all shares beneficially
owned by him or it, whether acquired before, in or after the IPO, in favor of such Business Combination.


 






    	 	 	 



    	 	 	 



    

 


2.             In the event that the Company fails to consummate a Business Combination within the time period set forth
in the Company’s Certificate of Incorporation, as the same may be amended from time to time, the undersigned will, as promptly
as possible, (i) cause the Trust Account to be liquidated and distributed to the holders of IPO Shares and (ii) cause the Company
to liquidate as soon as reasonably practicable. The undersigned hereby waives any
and all right, title, interest or claim of any kind in or to any distribution of the Trust Account and any remaining net assets
of the Company as a result of such liquidation with respect to the shares of Founders’ Common Stock owned by the undersigned
(“Claim”) and hereby waives any Claim the undersigned may have in the future as a result of, or arising out of, any
contracts or agreements with the Company and will not seek recourse against the Trust Account for any reason whatsoever. The undersigned
acknowledges and agrees that there will be no distribution from the Trust Account with respect to any warrants, all rights of which
will terminate on the Company’s liquidation.


 


3.             The undersigned acknowledges and agrees that prior to entering into a Business Combination with a target business that is affiliated
with any Insiders of the Company or their affiliates, such transaction must be approved by a majority of the Company’s disinterested
independent directors and the Company must obtain an opinion from an independent investment banking firm that such Business Combination
is fair to the Company’s unaffiliated stockholders from a financial point of view.


 


4.             Neither
the undersigned, any member of the family of the undersigned, nor any affiliate of the undersigned will be entitled to receive
and will not accept any compensation or other cash payment prior to, or for services rendered in order to effectuate, the consummation
of the Business Combination; provided that the Company shall be allowed to make the payments set forth in the Registration Statement
under the caption “Prospectus Summary – The Offering – Limited payments to insiders.”


 


5.             Neither
the undersigned, any member of the family of the undersigned, nor any affiliate of the undersigned will be entitled to receive
or accept a finder’s fee or any other compensation in the event the undersigned, any member of the family of the undersigned
or any affiliate of the undersigned originates a Business Combination.


 


6.           (a)           The
undersigned will place into escrow all shares of Founders’ Common Stock, portions of which shall be subject to forfeiture
in the event the Underwriters do not exercise their over-allotment option in full, pursuant to the terms of a Stock Escrow Agreement
which the Company will enter into with the undersigned and an escrow agent.


 






    	 	2	 



    	 	 	 



    

 


(b)           The undersigned will not, without the prior written consent of the Representatives pursuant to the Underwriting Agreement, offer,
sell, contract to sell, pledge, hedge, or otherwise dispose of, (or enter into any transaction which is designed to, or might
reasonably be expected to, result in the disposition (whether by actual disposition or effective economic disposition due to cash
settlement or otherwise) by the undersigned or any affiliate of the undersigned or any person in privity with the undersigned
or any affiliate of the undersigned), directly or indirectly, including the filing (or participation in the filing) of a registration
statement with the Securities and Exchange Commission in respect of, or establish or increase a put equivalent position or liquidate
or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and
the rules and regulations of the Securities and Exchange Commission promulgated thereunder with respect to, any Units, shares
of Common Stock, Warrants of the Company or any securities convertible into, or exercisable or exchangeable for shares of Common
Stock, or publicly announce an intention to effect any such transaction, for a period of 180 days after the date of the Underwriting
Agreement.


 


(c)           The
undersigned agrees that until the Company consummates a Business Combination, the undersigned’s Founders’ Warrants
will be subject to the transfer restrictions described in the Founder Warrants Purchase Agreement relating to the undersigned’s
Founders’ Warrants.


 


(d)           The
undersigned acknowledges and agrees that if, in order to consummate any Business Combination, the holders of shares of Founders’
Common Stock or Founders’ Warrants are required to transfer, sell or assign a portion of such securities to a third party,
or contribute back to the capital of the Company a portion of any such securities to be cancelled by the Company, the undersigned
will transfer, sell or assign to such third party, or contribute back to the capital of the Company, at no cost, a proportionate
number of shares of Founders’ Common Stock or Founders’ Warrants, as applicable, pro rata with the other holders of
shares of Founders’ Common Stock or Founders’ Warrants, as applicable.


 


7.            (a)           In
order to minimize potential conflicts of interest that may arise from multiple corporate affiliations, the undersigned hereby
agrees that until the earliest of the Company’s initial Business Combination or liquidation, the undersigned shall present
to the Company for its consideration, prior to presentation to any other entity, any target business that has a fair market value
of at least 80% of the assets held in the Trust Account (excluding deferred underwriting commissions and taxes payable on the
income accrued on the Trust Account), subject to any pre-existing fiduciary or contractual obligations the undersigned might have.


 


(b)           The
undersigned has agreed not to participate in the formation of, or become an officer or director of, any blank check company (except
as a passive investor) until the Company has entered into a definitive agreement regarding its initial Business Combination or
the Company has failed to complete an initial Business Combination within the time period set forth in the Company’s Certificate
of Incorporation as the same may be amended from time to time.


 






    	 	3	 



    	 	 	 



    

 


(c)           The
undersigned hereby agrees and acknowledges that (i) each of the Underwriters and the Company would be irreparably injured in the
event of a breach of the obligations under paragraphs 7(a) and/or 7(b) herein, (ii) monetary damages may not be an adequate remedy
for such breach and (iii) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that
such party may have in law or in equity, in the event of such breach.


 


8.            The undersigned agrees to be a Director of the Company until the earlier of the consummation by the Company of a Business Combination or the liquidation of the Company.  The undersigned's biographical information previously furnished to the Company and the Representatives is true and accurate in all respects, does not omit any material information with respect to the undersigned's background and contains all of the information required to be disclosed pursuant to Item 401 of Regulation S-K, promulgated under the Securities Act.  The undersigned's FINRA Questionnaire previously furnished to the Company and the Representatives is true and accurate in all respects.  The undersigned represents and warrants that:


 


(a)           he
is not subject to, or a respondent in, any legal action for, any injunction, cease-and-desist order or order or stipulation to
desist or refrain from any act or practice relating to the offering of securities in any jurisdiction;




 


(b)           he
has never been convicted of or pleaded guilty to any crime (i) involving any fraud or (ii) relating to any financial transaction
or handling of funds of another person, or (iii) pertaining to any dealings in any securities and he is not currently a defendant
in any such criminal proceeding; and




 


(c)           he
has never been suspended or expelled from membership in any securities or commodities exchange or association or had a securities
or commodities license or registration denied, suspended or revoked.




 


9.             The undersigned has full right and power, without violating any agreement by which he is bound, to enter into this letter agreement and to serve as a Director.


 


10.           The undersigned hereby waives any right to exercise conversion rights with respect to any shares of the Company’s common
stock owned or to be owned by the undersigned, directly or indirectly, whether such shares be part of the Founders’ Common
Stock or shares purchased by the undersigned in the IPO or in the aftermarket, and each agrees not to seek conversion with respect
to such shares in connection with any vote to approve a Business Combination.


  


11.           The undersigned hereby agrees to not propose, or vote in favor of, an amendment to Article Sixth of the Company’s Amended
and Restated Certificate of Incorporation prior to the consummation of a Business Combination unless the Company provides public
stockholders with the opportunity to convert their shares of common stock upon such approval in accordance with such Article Sixth
thereof.


 






    	 	4	 



    	 	 	 



    

 


12.           [Intentionally Omitted].


 


13.           This
letter agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without
giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The undersigned hereby (i) agrees that any action, proceeding or claim against him arising out of or relating in any way
to this letter agreement (a “Proceeding”) shall be brought and enforced in the courts of the State of New York of
the United States of America for the Southern District of New York, and irrevocably submits to such jurisdiction, which jurisdiction
shall be exclusive, (ii) waives any objection to such exclusive jurisdiction and that such courts represent an inconvenient forum
and (iii) irrevocably agrees to appoint Graubard Miller as agent for the service of process in the State of New York to receive,
for the undersigned and on his behalf, service of process in any Proceeding. If for any reason such agent is unable to act as
such, the undersigned will promptly notify the Company and the Representatives and appoint a substitute agent acceptable to each
of the Company and the Representatives within 30 days and nothing in this letter will affect the right of either party to serve
process in any other manner permitted by law.


 


14.           As
used herein, (i) a “Business Combination” shall mean a merger, share exchange, asset acquisition, stock purchase,
recapitalization, reorganization or other similar business combination with one or more businesses or entities; (ii) “Insiders”
shall mean all officers, directors and sponsors of the Company immediately prior to the IPO; (iii) “Founders’ Common
Stock” shall mean all of the shares of Common Stock of the Company acquired by an Insider prior to the IPO; (iv) “IPO
Shares” shall mean the shares of Common Stock issued in the Company’s IPO; (v) “Founders’ Warrants”
shall mean the warrants that are being sold privately by the Company simultaneously with the consummation of the IPO; (vi) “Trust
Account” shall mean the trust account into which a portion of the net proceeds of the Company’s IPO will be deposited;
and (vii) “Registration Statement” means the Company’s registration statement on Form S-1 (SEC File No. 333-206693)
filed with the Securities and Exchange Commission.


 


15.           This
Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof
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 changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except
by a written instrument executed by all parties hereto.


 


16.           The undersigned acknowledges and understands that the Underwriters and the Company will rely upon the agreements, representations
and warranties set forth herein in proceeding with the IPO. Nothing contained herein shall be deemed to render the Underwriters
a representative of, or a fiduciary with respect to, the Company, its stockholders or any creditor or vendor of the Company with
respect to the subject matter hereof.


 






    	 	5	 



    	 	 	 



    

 


17.           This
letter agreement shall be binding on the undersigned and such person’s respective successors, heirs, personal representatives
and assigns. This letter agreement shall terminate on the earlier of (i) the consummation of a Business Combination and (ii) the
liquidation of the Company; provided, that such termination shall not relieve the undersigned from liability for any breach
of this agreement prior to its termination.


 


[Signature
Page Follows]


 




    	 	6	 



    	 	 	 



    



 


	 	 	
	 	 	Print
    Name of Insider
	 	 	 
	 	 	
	 	 	Signature
	 	 	 
	 	 	Acknowledged
    and Agreed:
	 	 	 
	 	 	Capitol
    Acquisition Corp. III
	 	 	 
	 	By:	/s/ L. Dyson Dryden
	 	 	Name: L. Dyson Dryden




	 	 	Title:   Chief Financial Officer






 


 


7