EX-10.4





 Exhibit 10.4 

PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT 

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT, dated as of February 23, 2021 (as it may from time to time be amended and including
all exhibits referenced herein, this “Agreement”), is entered into by and among Hudson Executive Investment Corp. III, a Delaware corporation (the “Company”), and HEC Sponsor III LLC, a Delaware limited liability
company (the “Purchaser”). 
 WHEREAS, the Company intends to consummate an initial public offering of the Company’s
units (the “Public Offering”), each unit consisting of one share of the Company’s Class A common stock, par value $0.0001 per share (each, a “Share”), and one-fifth
of one redeemable warrant. Each whole warrant entitles the holder to purchase one Share at an exercise price of $11.50 per Share. The Purchaser has agreed to purchase an aggregate of 8,333,333 warrants (or 9,383,333 warrants in the aggregate to the
extent the over-allotment option in connection with the Public Offering is exercised) (the “Private Placement Warrants”), each Private Placement Warrant entitling the holder to purchase one Share at an exercise price of $11.50 per
Share. 
 NOW THEREFORE, in consideration of the mutual promises contained in this Agreement and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as follows: 

AGREEMENT 
 Section 1.
Authorization, Purchase and Sale; Terms of the Private Placement Warrants. 
 A. Authorization of the Private Placement Warrants.
The Company has duly authorized the issuance and sale of the Private Placement Warrants to the Purchaser. 
 B. Purchase and Sale of the
Private Placement Warrants. 
 On the date of the consummation of the Public Offering or on such earlier time and date as may be
mutually agreed by the Purchaser and the Company (the “Initial Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, an aggregate of 8,333,333 Private Placement
Warrants at a price of $1.50 per warrant for an aggregate purchase price of $12,500,000 (the “Purchase Price”), which shall be paid by wire transfer of immediately available funds to the Company in accordance with the Company’s
wiring instructions at least one business day prior to the Initial Closing Date. On the Initial Closing Date, the Company, shall either, at its option, deliver certificates evidencing the Private Placement Warrants purchased by the Purchaser on such
date duly registered in the Purchaser’s name to the Purchaser, or effect such delivery in book-entry form. On the date of the consummation of the closing of the over-allotment option in connection with the Public Offering or on such earlier
time and date as may be mutually agreed by the Purchaser and the Company (each such date, an “Over-allotment Closing Date,” and each Over-allotment Closing Date (if any) and the Initial Closing Date being sometimes referred to
herein as a “Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to an aggregate of 1,050,000 Private Placement Warrants, in the same proportion as the amount of
the over-allotment option that is exercised, at a price of $1.50 per warrant for an aggregate purchase 












 
price of up to $1,575,000 (if the over-allotment option in connection with the Public Offering is exercised in full) (the “Over-allotment Purchase Price”), which shall be paid by
wire transfer of immediately available funds to the Company in accordance with the Company’s wiring instructions at least one business day prior to each Over-Allotment Closing Date. On the Over-allotment Closing Date, upon the payment by the
Purchaser of the Overallotment Purchase Price payable by them by wire transfer of immediately available funds to the Company, the Company shall either, at its option, deliver certificates evidencing the Private Placement Warrants purchased by the
Purchaser on such date duly registered in the Purchaser’s name to the Purchaser, or effect such delivery in book-entry form. 
 C.
Terms of the Private Placement Warrants. 
 (i) The Private Placement Warrants shall have their terms set forth in a Warrant
Agreement to be entered into by the Company and a warrant agent, in connection with the Public Offering (a “Warrant Agreement”). 

(ii) At or prior to the time of the Initial Closing Date, the Company and the Purchaser shall enter into a registration rights agreement (the
“Registration Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private Placement Warrants and the Shares underlying the Private Placement Warrants. 

Section 2. Representations and Warranties of the Company. As a material inducement to the Purchaser to enter
into this Agreement and purchase the Private Placement Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall survive each Closing Date) that: 

A. Organization and Corporate Power. The Company is a corporation duly organized, validly existing and in good standing under the laws
of the State of Delaware and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, operating results or assets of the Company.
The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement. 

B. Authorization; No Breach. 

(i) The execution, delivery and performance of this Agreement and the Private Placement Warrants have been duly authorized and approved by the
Company as of each Closing Date. This Agreement constitutes a valid and binding obligation of the Company, enforceable in accordance with its terms. Upon each issuance of Private Placement Warrants in accordance with, and payment pursuant to, the
terms of the Warrant Agreement and this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms. 

(ii) The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of the Private
Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment of, and compliance with, the respective terms hereof and thereof by the Company, do not and will not as of each Closing Date
(a) conflict with or result in a breach of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s capital stock
or assets under, (d) result 

  
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in a violation of, or (e) require any authorization, consent, approval, exemption, action, notice, declaration or filing, in each case, by or to any court or administrative or governmental
body or agency pursuant to the certificate of incorporation or the bylaws of the Company (in effect on the date hereof or as may be amended prior to completion of the contemplated Public Offering), or any material law, statute, rule or regulation to
which the Company is subject, or any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof under federal or state securities laws. 

C. Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, the
Placement Warrants will be duly and validly issued and the Shares issuable upon exercise of the Private Placement Warrants will be duly and validly issued, fully paid and nonassessable. On the date of issuance of the Placement Warrants, the Shares
issuable upon exercise of the Placement Warrants shall have been reserved for issuance. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, each Purchaser will have good title to the Private
Placement Warrants and the Shares issuable upon exercise of such Private Placement Warrants, free and clear of all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and under the other agreements
contemplated hereby, (ii) transfer restrictions under federal and state securities laws, and (iii) liens, claims or encumbrances imposed due to the actions of either Purchaser. 

D. Governmental Consents. No permit, consent, approval or authorization of, or declaration to or filing with, any governmental
authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other transactions contemplated hereby. 

Section 3. Representations and Warranties of the Purchaser. As a material inducement to the Company to enter
into this Agreement and issue and sell the Private Placement Warrants to the Purchaser, the Purchaser hereby, severally and not jointly, represents and warrants to the Company (which representations and warranties shall survive each Closing Date)
that: 
 A. Organization and Requisite Authority. The Purchaser possesses all requisite power and authority necessary to carry out
the transactions contemplated by this Agreement. 
 B. Authorization; No Breach. 

(i) This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to
bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or
law). 
 (ii) The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by
the Purchaser does not and shall not as of each Closing Date conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of any agreement, instrument, order, judgment or decree to which the Purchaser is subject that
would materially impact its ability to perform its obligations hereunder. 

  
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 C. Investment Representations. 

(i) The Purchaser is acquiring the Private Placement Warrants and, upon exercise of the Private Placement Warrants, the Shares issuable upon
such exercise (collectively, the “Securities”), will be acquired for the Purchaser’s own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution
thereof. 
 (ii) The Purchaser is an “accredited investor” as such term is defined in Rule 501(a)(3) of Regulation D of the
Securities Act of 1933, as amended (the “Securities Act”), and the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 

(iii) The Purchaser understands that the Securities are being offered and will be sold to it in reliance on specific exemptions from the
registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the representations and warranties of the Purchaser set forth
herein in order to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities. 
 (iv)
The Purchaser did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under the Securities Act. 

(v) The Purchaser has been furnished with all materials relating to the business, finances and operations of the Company and materials
relating to the offer and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions of the executive officers and directors of the Company. The Purchaser understands that its
investment in the Securities involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed investment decision with respect to the acquisition of the Securities. 

(vi) The Purchaser understands that no United States federal or state agency or any other government or governmental agency has passed on or
made any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Securities. 

(vii) The Purchaser understands that: (a) the Securities have not been and are not being registered under the Securities Act or any state
securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold in reliance on an exemption therefrom; and (b) except as specifically set forth in the
Registration Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder.
While the Purchaser understands that Rule 144 under the Securities Act is not available for the resale of securities initially issued by shell companies (other than business combination related shell companies) or issuers that have been at any time
previously a shell company, the Purchaser understands that Rule 144 includes an exception to this prohibition if the following conditions are met: (i) the issuer of the securities that was formerly a shell company has ceased to be a shell
company; (ii) the issuer of the securities is subject to the reporting requirements of Section 13 

  
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or 15(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”); (iii) the issuer of the securities has filed all Exchange Act reports and material required to
be filed, as applicable, during the preceding 12 months (or such shorter period that the issuer was required to file such reports and materials), other than Form 8-K reports; and (iv) at least one year
has elapsed from the time that the issuer filed current Form 10 type information with the SEC reflecting its status as an entity that is not a shell company. 

(viii) The Purchaser has knowledge and experience in financial and business matters, understands the high degree of risk associated with
investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to bear the economic risk of an investment in the Securities in the
amount contemplated hereunder for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies and will have no current or anticipated future needs for liquidity which would be
jeopardized by the investment in the Securities. The Purchaser can afford a complete loss of its investment in the Securities. 

Section 4. Conditions of the Purchaser’s Obligations. The obligations of the Purchaser to purchase and
pay for the Private Placement Warrants are subject to the fulfillment, on or before each Closing Date, of each of the following conditions: 

A. Representations and Warranties. The representations and warranties of the Company contained in Section 2 shall be true and
correct at and as of such Closing Date as though then made. 
 B. Performance. The Company shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before such Closing Date. 

C. No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted,
entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the
transactions contemplated by this Agreement or the Warrant Agreement. 
 D. Warrant Agreement and Registration Rights Agreement. The
Company shall have entered into the Warrant Agreement and the Registration Rights Agreement, each on terms satisfactory to the Purchaser. 

E. Corporate Consents. The Company shall have obtained the consent of its Board of Directors authorizing the execution, delivery and
performance of this Agreement and the Warrant Agreement and the issuance and sale of the Private Placement Warrants hereunder. 

Section 5. Conditions of the Company’s Obligations. The obligations of the Company to the Purchaser
under this Agreement are subject to the fulfillment, on or before each Closing Date, of each of the following conditions: 
 A.
Representations and Warranties. The representations and warranties of the Purchaser contained in Section 3 shall be true and correct at and as of such Closing Date as though then made. 

  
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 B. Performance. The Purchaser shall have performed and complied with all agreements,
obligations and conditions contained in this Agreement that are required to be performed or complied with by the Purchaser on or before such Closing Date. 

C. Corporate Consents. The Company shall have obtained the consent of its Board of Directors authorizing the execution, delivery and
performance of this Agreement and the Warrant Agreement and the issuance and sale of the Private Placement Warrants hereunder. 
 D. No
Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any
self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement. 

E. Warrant Agreement. The Company shall have entered into the Warrant Agreement on terms satisfactory to the Company. 

Section 6. Termination. This Agreement may be terminated at any time after December 31, 2021 upon the
election by either the Company or the Purchaser upon written notice to the other party if the closing of the Public Offering does not occur prior to such date. 

Section 7. Survival of Representations and Warranties. All of the representations and warranties contained
herein shall survive each Closing Date. 
 Section 8. Definitions. Terms used but not otherwise defined in
this Agreement shall have the meaning assigned to such terms in the registration statement on Form S-1 the Company plans to file with the U.S. Securities and Exchange Commission under the Securities Act. 

Section 9. Miscellaneous. 

A. Successors and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by
or on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not
assign this Agreement without the prior written consent of the other party hereto, other than assignments by the Purchaser to its affiliates (including, without limitation, one or more of its members). 

B. Severability. Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid
under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of
this Agreement. 
 C. Counterparts. This Agreement may be executed simultaneously in two or more counterparts, none of which need
contain the signatures of more than one party, but all such counterparts taken together shall constitute one and the same agreement. In the event that any signature is delivered by facsimile transmission or by
e-mail delivery of a “pdf” format data file, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and
effect as if such facsimile or “.pdf” signature page were an original thereof. 

  
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 D. Descriptive Headings; Interpretation. The descriptive headings of this Agreement
are inserted for convenience only and do not constitute a substantive part of this Agreement. The use of the word “including” in this Agreement shall be by way of example rather than by limitation. 

E. Governing Law. This Agreement shall be deemed to be a contract made under the laws of the State of New York and for all purposes
shall be construed in accordance with the internal laws of the State of New York. 
 F. Amendments. This Agreement may not be
amended, modified or waived as to any particular provision, except by a written instrument executed by all parties hereto. 
 [Signature
Page Follows] 

  
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 IN WITNESS WHEREOF, the parties hereto have executed this Agreement to be effective
as of the date first set forth above. 
  

			
	COMPANY:
	
	HUDSON EXECUTIVE INVESTMENT CORP. III, a Delaware corporation
		
	By:	 	 /s/ Jonathan Dobres

		 	Name: Jonathan Dobres
		 	Title: Chief Financial Officer
	
	PURCHASER:
	
	HEC SPONSOR III LLC, a Delaware limited liability company
		
	By:	 	 /s/ Douglas G. Bergeron

		 	Name: Douglas G. Bergeron
		 	Title: Manager


 [Signature Page to Private Placement Warrants Purchase Agreement]