Exhibit 4.4


 


WARRANT AGENT AGREEMENT


 


This Warrant Agent Agreement (this “Agreement”)
is made effective as of April 2, 2018, by and between Zion Oil & Gas, Inc., a Delaware corporation having its principal place
of business at 12655 North Central Expressway, Suite 1000, Dallas, Texas 75243 (the “Company”), and American
Stock Transfer & Trust Company, LLC, a New York limited liability trust company with offices at 6201 15th Avenue,
Brooklyn, NY 11219 (“AST”) and is an amendment to the Warrant Agent Agreement dated August 1, 2014 between
the Company and AST, to the February 2, 2015 amendment to the Warrant Agent Agreement, to the November 1, 2016 amendment to the
Warrant Agent Agreement, to the May 22, 2017 amendment to the Warrant Agent Agreement, to the October 12, 2017 amendment to the
Warrant Agent Agreement and to the February 1, 2018 amendment to the Warrant Agent Agreement. 


 


WHEREAS, the Company
is offering through AST (as also the “Subscription Agent”), at no cost, non-transferable Subscription
Rights to purchase Rights (each “Right” and collectively the “Rights”) of its securities to persons who
owned shares of the Company’s Common Stock on March 12, 2018 (the “Record Date”), with each Right
consisting of one (1) share of Common Stock, par value $0.01 per share and one (1) Common Stock Purchase Warrant to purchase an
additional one (1) share of Common Stock. Each Right may be purchased at a per Right subscription price of $5.00. Each Warrant
affords the investor the opportunity to purchase one share of Common Stock at a warrant exercise price of $3.00. The warrants will
have the symbol “ZNWAI.” The warrants will become exercisable on June 29, 2018 (the “Warrant Exercise
Date”) and will continue to be exercisable for one (1) year after the Exercise date.


 


WHEREAS, shareholders
will receive 0.10 (one tenth) of a subscription right (i.e., ONE subscription right for each TEN shares) for each
share of Common Stock that is owned on March 12, 2018. The subscription rights will expire, if they are not exercised by 5:00 p.m.,
Eastern Standard Time, on May 31, 2018 (“Expiration Date”).


 


WHEREAS, the Company is utilizing the Registration
Statement on Form S-3 (Registration No. 333-216191), as amended, which was declared effective by the SEC on March 10, 2017 (the
“Registration Statement”) and the Prospectus Supplement filed April 2, 2018 to facilitate the trading
of the shares of Common Stock included in the Rights Offering and the shares of Common Stock underlying the Warrants that are included
in the Rights as well as the Warrants;


 


WHEREAS, the shares of Common Stock included
in the Rights are tradable on the NASDAQ under the symbol ZN and, following the closing of the Rights Offering, the shares of Common
Stock underlying the Warrants, will be tradable after Warrant exercise on the NASDAQ under the symbol ZN;


 


WHEREAS, the Company desires AST to act
on behalf of the Company, and AST is willing to so act, in connection with the issuance, registration, transfer, exchange, redemption
and exercise of the Warrants (in such capacity, the “Warrant Agent”) herein described;


 


WHEREAS, the Company desires to provide
for the form and provisions of the Warrant, the terms upon which it shall be issued and exercised, and the respective rights, limitation
of rights, and immunities of the Company, the Warrant Agent, and the holders of the Warrants; and


 






    	 	 	 



     


    

 


WHEREAS, all acts and things have been done
and performed which are necessary to make the Warrants, when executed on behalf of the Company and countersigned by or on behalf
of the Warrant Agent, as provided herein, the valid, binding and legal obligations of the Company, and to authorize the execution
and delivery of this Agreement.


 


NOW, THEREFORE, in consideration of the
mutual agreements herein contained, the parties hereto agree as follows:


 


1. Appointment of Warrant Agent. The Company hereby
appoints the Warrant Agent to act as agent for the Company for the Warrants herein described, and the Warrant Agent hereby accepts
such appointment and agrees to perform the same in accordance with the terms and conditions set forth in this Agreement.


   


2. New Warrant.


 


2.1 Form of Warrant. The Warrant shall be issued
in registered form or held in book entry form by AST as Warrant Agent. The Warrant shall be in substantially the form of Exhibit
A hereto, the provisions of which are incorporated herein, and shall be signed by, or bear the facsimile signature of,
the Executive Chairman and Secretary/Treasurer of the Company and shall bear a facsimile of the Company’s seal. In the event the
person whose facsimile signature has been placed upon any Warrant shall have ceased to serve in the capacity in which such person
signed the Warrant before such Warrant is issued, it may be issued with the same effect as if he or she had not ceased to be such
at the date of issuance.


 


2.2 Effect of Countersignature. Unless and until
countersigned by the Warrant Agent pursuant to this Agreement, a Warrant shall be invalid and of no effect and may not be exercised
by the holder thereof, unless acknowledged and held in book entry form by the Warrant Agent.


 


2.3 Registration.


 


2.3.1 Warrant Register. The Warrant Agent shall
maintain books (“Warrant Register” or also referred to as “book entry form”)
for the registration of original issuance and the registration of transfer of the Warrants, if the Warrants are not held in book
entry form by Warrant Agent. Upon the initial issuance of the Warrants unless held in book entry form by the Warrant Agent, the
Warrant Agent shall issue and register the Warrants in the names of the respective holders thereof in such denominations and otherwise
in accordance with instructions delivered to the Warrant Agent by the Company.


 


2.3.2 Registered Holder. Prior to due presentment
for registration of transfer of any Warrant, the Company and the Warrant Agent may deem and treat the person in whose name such
Warrant shall be registered upon the Warrant Register (“registered holder”), as the absolute owner of such
Warrant and of each Warrant represented thereby (notwithstanding any notation of ownership or other writing on the Warrant Certificate
made by anyone other than the Company or the Warrant Agent), for the purpose of any exercise thereof, and for all other purposes,
and neither the Company nor the Warrant Agent shall be affected by any notice to the contrary.


 


3. Terms and Exercise of Warrants.


 


3.1 Warrant Price. Each Warrant shall, when countersigned
by the Warrant Agent, entitle the registered holder thereof, subject to the provisions of such Warrant and this Warrant Agreement,
to purchase from the Company the number of shares of Common Stock stated therein, at the price of $3.00 per share, subject to the
adjustments provided in this Section 3.1 and Section 4 hereof. The term “Warrant Price” as used in this Warrant Agreement
refers to the price per share at which Common Stock may be purchased at the time a Warrant is exercised. The Company in its sole
discretion may lower the Warrant Price at any time prior to the Expiration Date for a period of not less than ten business days,
provided that any such reduction shall be identical among all of the Warrants.


 






    	 	2	 



     


    

 


3.2 Duration of Warrants. A Warrant may be exercised
only during the period commencing on June 29, 2018 and continue to be exercisable for one (1) year after the exercise date, terminating
at 5:00 p.m., Eastern Standard Time. Notwithstanding the foregoing, no Warrant shall be exercisable unless, at the time of exercise,
a registration statement relating to the Common Stock issuable upon the exercise of such Warrant is effective and current and a
prospectus is available for use by the holders thereof and the Common Stock has been qualified or deemed to be exempt under the
securities laws of the state of residence of the holder of such Warrants. The period during which a Warrant may be exercised shall
be deemed the “Exercise Period” and the termination of such Exercise Period shall be deemed the “Expiration
Date.” Each Warrant not exercised on or before the Expiration Date shall become void, and all rights thereunder and
all rights in respect thereof under this Agreement shall cease at the close of business on the Expiration Date. The Company in
its sole discretion may extend the duration of the Warrants by delaying the Expiration Date; provided, however, the Company will
provide notice to registered holders of the Warrants of such extension of not less than 20 days and, further provided that any
such extension shall be identical in duration among all of the Warrants.


  


3.3 Exercise of Warrants.


 


3.3.1 Payment. Subject to the provisions of the
Warrants and this Agreement, a Warrant, when countersigned by the Warrant Agent, may be exercised by the registered holder thereof
by surrendering it at the office of the Warrant Agent, or at the office of its successor as Warrant Agent, in Brooklyn, New York,
with the subscription form, as set forth in the Warrant, or exercised by other electronic means acceptable to the Company, duly
executed by paying in full, by bank check, bank wire, other electronic bank payment method, or other legal currency means
of payment acceptable by the Company and payable to the order of the Company, the Warrant Price for each full share of Common Stock
as to which the Warrant is exercised and any and all applicable taxes due in connection with the exercise of the Warrant, the exchange
of the Warrant for the Common Stock and the issuance of the Common Stock.


 


3.3.2 Issuance of Certificates. As soon as practicable
after the exercise of any Warrant and the clearance of the funds in payment of the Warrant Price, the Company shall issue to the
registered holder of such Warrant a certificate or certificates for the number of full shares of Common Stock to which he, she
or it is entitled, registered in such name or names as may be directed by him, her or it, and if such Warrant shall not have been
exercised in full, a new countersigned Warrant for the number of shares as to which such Warrant shall not have been exercised,
unless the Common Stock is to be held in book entry form by AST without the issuance of a certificate and any remaining balance
of Warrants to be maintained in book entry form by the Warrant Agent. Notwithstanding the foregoing, the Company shall not be obligated
to deliver or to recognized in book entry form any securities pursuant to the exercise of a Warrant unless (i) a registration statement
under the Act with respect to the Common Stock issuable upon such exercise is effective, or (ii) in the opinion of counsel to the
Company, the exercise of the Warrants is exempt from the registration requirements of the Act and such securities are qualified
for sale or exempt from qualification under applicable securities laws of the states or other jurisdictions in which the registered
holders reside. Warrants may not be exercised by, or securities issued to, any registered holder in any state in which such exercise
or issuance would be unlawful. In no event will the Company be required to provide the registered holder of a warrant with a net-cash
settlement or other consideration in lieu of physical settlement in shares of Common Stock, regardless of whether the Common Stock underlying
the Warrants is registered pursuant to an effective registration statement.


 






    	 	3	 



     


    

 


3.3.3 Valid Issuance. All shares of Common Stock
issued upon the proper exercise of a Warrant in conformity with this Agreement shall be validly issued, fully paid and nonassessable.


 


3.3.4 Date of Issuance. Each person in whose name
any such certificate for shares of Common Stock is issued shall for all purposes be deemed to have become the holder of record
of such shares on the date on which the Warrant was surrendered and payment of the Warrant Price was made, irrespective of the
date of delivery of such certificate or the recording by book entry, except that, if the date of such surrender and payment is
a date when the stock transfer books of the Company are closed, such person shall be deemed to have become the holder of such shares
at the close of business on the next succeeding date on which the stock transfer books are open.


 


4. Adjustments.


 


4.1 Stock Dividends Split Ups. If after the date
hereof, and subject to the provisions of Section 4.6 below, the number of outstanding shares of Common Stock is increased by a
stock dividend payable in shares of Common Stock, or by a split up of shares of Common Stock, or other similar event, then, on
the effective date of such stock dividend, split up or similar event, the number of shares of Common Stock issuable on exercise
of each Warrant shall be increased in proportion to such increase in outstanding shares of Common Stock. For purposes of clarification,
no adjustment shall be made in the event of a rights offering, or a distribution of rights treated as a dividend to all shareholders
of record, or similar transactions.


 


4.2 Aggregation of Shares. If after the date hereof,
and subject to the provisions of Section 4.6, the number of outstanding shares of Common Stock is decreased by a consolidation,
combination, reverse stock split or reclassification of shares of Common Stock or other similar event, then, on the effective date
of such consolidation, combination, reverse stock split, reclassification or similar event, the number of shares of Common Stock
issuable on exercise of each Warrant shall be decreased in proportion to such decrease in outstanding shares of Common Stock.


   


4.3 Adjustments in Exercise Price. Whenever the
number of shares of Common Stock purchasable upon the exercise of the Warrants is adjusted, as provided in Section 4.1 and 4.2
above, the Warrant Price shall be adjusted (to the nearest cent) by multiplying such Warrant Price immediately prior to such adjustment
by a fraction (x) the numerator of which shall be the number of shares of Common Stock purchasable upon the exercise of the Warrants
immediately prior to such adjustment, and (y) the denominator of which shall be the number of shares of Common Stock so purchasable
immediately thereafter.


 






    	 	4	 



     


    

 


4.4 Replacement of Securities upon Reorganization,
etc. In case of any reclassification or reorganization of the outstanding shares of Common Stock (other than a change covered
by Section 4.1 or 4.2 hereof or that solely affects the par value of such shares of Common Stock), or in the case of any merger
or consolidation of the Company with or into another corporation (other than a consolidation or merger in which the Company is
the continuing corporation and that does not result in any reclassification or reorganization of the outstanding shares of Common
Stock), or in the case of any sale or conveyance to another corporation or entity of the assets or other property of the Company
as an entirety or substantially as an entirety in connection with which the Company is dissolved, the Warrant holders shall thereafter
have the right to purchase and receive, upon the basis and upon the terms and conditions specified in the Warrants and in lieu
of the shares of Common Stock of the Company immediately theretofore purchasable and receivable upon the exercise of the rights
represented thereby, the kind and amount of shares of stock or other securities or property (including cash) receivable upon such
reclassification, reorganization, merger or consolidation, or upon a dissolution following any such sale or transfer, that the
Warrant holder would have received if such Warrant holder had exercised his, her or its Warrant(s) immediately prior to such event;
and if any reclassification also results in a change in shares of Common Stock covered by Section 4.1 or 4.2, then such adjustment
shall be made pursuant to Sections 4.1, 4.2, 4.3 and this Section 4.4. The provisions of this Section 4.4 shall similarly
apply to successive reclassifications, reorganizations, mergers or consolidations, sales or other transfers.


 


4.5 Notices of Changes in Warrant. Upon every
adjustment of the Warrant Price or the number of shares issuable on exercise of a Warrant, the Company shall give written notice
thereof to the Warrant Agent, which notice shall state the Warrant Price resulting from such adjustment and the increase or decrease,
if any, in the number of shares purchasable at such price upon the exercise of a Warrant, setting forth in reasonable detail the
method of calculation and the facts upon which such calculation is based. Upon the occurrence of any event specified in Sections
4.1, 4.2, 4.3 or 4.4, then, in any such event, the Company shall give written or electronic notice to the Warrant holder, at the
last address set forth for such holder in the Warrant Register, of the record date or the effective date of the event. Failure
to give such notice, or any defect therein, shall not affect the legality or validity of such event.


 


4.6  Form of Warrant. The form of Warrant need not
be changed because of any adjustment pursuant to this Section 4, and Warrants issued after such adjustment may state the same Warrant
Price and the same number of shares as is stated in the Warrants initially issued pursuant to this Agreement. However, the Company
may at any time in its sole discretion make any change in the form of Warrant that the Company may deem appropriate and that does
not affect the substance thereof, and any Warrant thereafter issued or countersigned, whether in exchange or substitution for an
outstanding Warrant or otherwise, may be in the form as so changed.


   


5. Transfer and Exchange of Warrants.


 


5.1 Registration of Transfer. The Warrant Agent
shall register the transfer, from time to time, of any outstanding Warrant upon the Warrant Register, upon surrender of such Warrant
for transfer, properly endorsed with signatures properly guaranteed and accompanied by appropriate instructions for transfer. Upon
any such transfer, a new Warrant representing an equal aggregate number of Warrants shall be issued and the old Warrant shall be
cancelled by the Warrant Agent. The Warrants so cancelled shall be delivered by the Warrant Agent to the Company from time to time
upon request.


  


5.2 Procedure for Surrender of Warrants. Warrants
may be surrendered to the Warrant Agent, together with a written request for exchange, and thereupon the Warrant Agent shall issue
in exchange therefor one or more new Warrants as requested by the registered holder of the Warrants so surrendered, representing
an equal aggregate number of Warrants; provided, however, in the event a Warrant surrendered for transfer bears a restrictive legend,
the Warrant Agent shall not cancel such Warrant and issue new Warrants in exchange therefor until the Warrant Agent has received
an opinion of counsel for the Company stating such transfer may be made and indicating whether the new Warrants must also bear
a restrictive legend. Book-entry held warrants may be surrendered electronically by any means acceptable to the Company.


 






    	 	5	 



     


    

 


5.3 Fractional Warrants. The Warrant Agent shall
not be required to effect any registration of transfer or exchange which will result in the issuance of a warrant certificate for
a fraction of a warrant.


 


5.4 Service Charges. No service charge shall be
made for any exchange or registration of transfer of Warrants.


 


5.5 Warrant Execution and Countersignature. The
Warrant Agent is hereby authorized to countersign and deliver, in accordance with the terms of this Agreement, the Warrants required
to be issued pursuant to the provisions of this Section 5, and the Company, whenever required by the Warrant Agent, will supply
the Warrant Agent with Warrants duly executed on behalf of the Company for such purpose.


 


6. Other Provisions Relating to Rights of Holders
of Warrants.


 


6.1 No Rights as Stockholder. A Warrant does not
entitle the registered holder thereof to any of the rights of a stockholder of the Company, including, without limitation, the
right to receive dividends, or other distributions, exercise any preemptive rights to vote or to consent or to receive notice as
stockholders in respect of the meetings of stockholders or the election of directors of the Company or any other matter.


 


6.2 Lost, Stolen, Mutilated, or Destroyed Warrants.
If any Warrant is lost, stolen, mutilated, or destroyed, the Company and the Warrant Agent may on such terms as to indemnity or
otherwise as they may in their discretion impose (which shall, in the case of a mutilated Warrant, include the surrender thereof),
issue a new Warrant of like denomination, tenor, and date as the Warrant so lost, stolen, mutilated, or destroyed. Any such new
Warrant shall constitute a substitute contractual obligation of the Company, whether or not the allegedly lost, stolen, mutilated,
or destroyed Warrant shall be at any time enforceable by anyone.


 


6.3 Reservation of Common Stock. The Company shall
at all times reserve and keep available a number of its authorized but unissued shares of Common Stock that will be sufficient
to permit the exercise in full of all outstanding Warrants issued pursuant to this Agreement.


   


7. Concerning the Warrant Agent and Other Matters.


 


7.1 Payment of Taxes. The Company will from time
to time promptly pay all taxes and charges that may be imposed upon the Company or the Warrant Agent in respect of the issuance
or delivery of shares of Common Stock upon the exercise of Warrants, but the Company shall not be obligated to pay any transfer
taxes in respect of the Warrants or such shares.


 






    	 	6	 



     


    

 


7.2 Resignation, Consolidation, or Merger of Warrant
Agent.


 


7.2.1 Appointment of Successor Warrant Agent.
The Warrant Agent, or any successor to it hereafter appointed, may resign its duties and be discharged from all further duties
and liabilities hereunder after giving sixty (60) days’ notice in writing to the Company. If the office of the Warrant Agent becomes
vacant by resignation or incapacity to act or otherwise, the Company shall appoint in writing a successor Warrant Agent in place
of the Warrant Agent. If the Company shall fail to make such appointment within a period of 30 days after it has been notified
in writing of such resignation or incapacity by the Warrant Agent or by the holder of the Warrant (who shall, with such notice,
submit his Warrant for inspection by the Company), then the holder of any Warrant may apply to a court of competent jurisdiction
for the appointment of a successor Warrant Agent. Any successor Warrant Agent, whether appointed by the Company or by such court,
shall be authorized to exercise corporate trust powers and subject to supervision or examination by federal or state authority.
After appointment, any successor Warrant Agent shall be vested with all the authority, powers, rights, immunities, duties, and
obligations of its predecessor Warrant Agent with like effect as if originally named as Warrant Agent hereunder, without any further
act or deed; but if for any reason it becomes necessary or appropriate, the predecessor Warrant Agent shall execute and deliver,
at the expense of the Company, an instrument transferring to such successor Warrant Agent all the authority, powers, and rights
of such predecessor Warrant Agent hereunder; and upon request of any successor Warrant Agent the Company shall make, execute, acknowledge,
and deliver any and all instruments in writing for more fully and effectually vesting in and confirming to such successor Warrant
Agent all such authority, powers, rights, immunities, duties, and obligations.


 


 7.2.2 Notice of Successor Warrant Agent.
In the event a successor Warrant Agent shall be appointed, the Company shall give notice thereof to the predecessor Warrant Agent
and the transfer agent for the Common Stock not later than the effective date of any such appointment.


 


7.2.3 Merger or Consolidation of Warrant Agent.
Any corporation into which the Warrant Agent may be merged or with which it may be consolidated or any corporation resulting from
any merger or consolidation to which the Warrant Agent shall be a party shall be the successor Warrant Agent under this Agreement
without any further act.


 


7.3 Fees and Expenses of Warrant Agent.


 


7.3.1 Remuneration. The Company agrees to pay
the Warrant Agent reasonable remuneration for its services as such Warrant Agent hereunder as set forth on Exhibit B
hereto, and will reimburse the Warrant Agent upon demand for all expenditures that the Warrant Agent may reasonably incur in the
execution of its duties hereunder.


 


7.3.2 Further Assurances. The Company agrees to
perform, execute, acknowledge, and deliver or cause to be performed, executed, acknowledged, and delivered all such further and
other acts, instruments, and assurances as may reasonably be required by the Warrant Agent for the carrying out or performing of
the provisions of this Warrant Agreement.


 


7.4 Liability of Warrant Agent.


 


7.4.1 Reliance on Company Statement. Whenever
in the performance of its duties under this Agreement, the Warrant Agent shall deem it necessary or desirable that any fact or
matter be proved or established by the Company prior to taking or suffering any action hereunder, such fact or matter (unless other
evidence in respect thereof be herein specifically prescribed) may be deemed to be conclusively proved and established by a statement
signed by the Chief Executive Officer, President, Chief Operating Officer, Chief Financial Officer, Executive Vice President, Treasurer,
or Secretary of the Company and delivered to the Warrant Agent. The Warrant Agent may rely upon such statement for any action taken
or suffered in good faith by it pursuant to the provisions of this Agreement.


 






    	 	7	 



     


    

  


7.4.2 Indemnity. The Warrant Agent shall be liable
hereunder only for its own gross negligence, willful misconduct or bad faith. The Company agrees to indemnify the Warrant Agent
and save it harmless against any and all liabilities, including judgments, costs and reasonable counsel fees, for anything done
or omitted by the Warrant Agent in the execution of this Agreement except as a result of the Warrant Agent’s gross negligence,
willful misconduct, or bad faith.


 


7.4.3 Exclusions. The Warrant Agent shall have
no responsibility with respect to the validity of this Agreement or with respect to the validity or execution of any Warrant (except
its countersignature thereof); nor shall it be responsible for any breach by the Company of any covenant or condition contained
in this Agreement or in any Warrant; nor shall it be responsible to make any adjustments required under the provisions of Section
4 hereof or responsible for the manner, method, or amount of any such adjustment or the ascertaining of the existence of facts
that would require any such adjustment; nor shall it by any act hereunder be deemed to make any representation or warranty as to
the authorization or reservation of any shares of Common Stock to be issued pursuant to this Agreement or any Warrant or as to
whether any shares of Common Stock will when issued be valid and fully paid and nonassessable.


  


7.5 Acceptance of Agency. The Warrant Agent hereby
accepts the agency established by this Agreement and agrees to perform the same upon the terms and conditions herein set forth
and among other things, shall account promptly to the Company with respect to Warrants exercised and concurrently account for,
and pay to the Company, all moneys received by the Warrant Agent for the purchase of shares of the Company’s Common Stock through
the exercise of Warrants.


 


7.6 Waiver. The Warrant Agent hereby waives any
and all right, title, interest or claim of any kind (“Claim”) in or to any distribution of any account
in which funds related to the purchase or exercise of the Warrants are held, and hereby agrees not to seek recourse, reimbursement,
payment or satisfaction for any Claim against any such account for any reason whatsoever.


 


8. Miscellaneous Provisions.


 


8.1 Successors. All the covenants and provisions
of this Agreement by or for the benefit of the Company or the Warrant Agent shall bind and inure to the benefit of their respective
successors and assigns.


 


8.2 Notices. Any notice or other communication
required or which may be given hereunder shall be in writing and either be delivered personally or by private national courier
service, or be mailed, certified or registered mail, return receipt requested, postage prepaid, and shall be deemed given when
so delivered personally or, if sent by private national courier service, on the next business day after delivery to the courier,
or, if mailed, two business days after the date of mailing, as follows:


 


Zion Oil & Gas, Inc.


12655 North Central Expressway, Suite 1000


Dallas, Texas 75243


Attn:  Corporate Secretary/Treasurer


 


Any notice, statement or demand authorized by this Agreement
to be given or made by the holder of any Warrant or by the Company to or on the Warrant Agent shall be sufficiently given when
so delivered if by hand or overnight delivery or if sent by certified mail or private courier service five days after deposit of
such notice, postage prepaid, addressed (until another address is filed in writing by the Warrant Agent with the Company), as follows:


 


American Stock Transfer & Trust Company, LLC


6201 15th Avenue


Brooklyn, New York 11219


Attn: Account Executive




 



    	 	8	 



     


    




 


8.3 Applicable Law. The validity, interpretation,
and performance of this Agreement and of the Warrants shall be governed in all respects by the laws of the State of New York, without
giving effect to conflict of laws. Each party hereby agrees that any action, proceeding or claim against it arising out of or relating
in any way to this Agreement shall be brought and enforced in the appropriate state or federal courts in the State of New York,
and irrevocably submits to such jurisdiction, which jurisdiction shall be exclusive. Each party hereby waives any objection to
such exclusive jurisdiction and that such courts represent an inconvenient forum.


 


8.4 Persons Having Rights under this Warrant Agreement.
Nothing in this Agreement expressed and nothing that may be implied from any of the provisions hereof is intended, or shall be
construed, to confer upon, or give to, any person or corporation other than the parties hereto and the registered holders of the
Warrants, any right, remedy, or claim under or by reason of this Agreement or of any covenant, condition, stipulation, promise,
or agreement hereof. All covenants, conditions, stipulations, promises, and agreements contained in this Agreement shall be for
the sole and exclusive benefit of the parties hereto and their successors and assigns and of the registered holders of the Warrants. 


 


 8.5 Examination of the Warrant Agent Agreement.
A copy of this Agreement shall be available at all reasonable times at the office of the Warrant Agent for inspection by the registered
holder of any Warrant. The Warrant Agent may require any such holder to submit his Warrant for inspection by it.


 


8.6 Counterparts. This Agreement may be executed
in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts
shall together constitute but one and the same instrument.


 


8.7 Effect of Headings. The Section headings herein
are for convenience only and are not part of this Agreement and shall not affect the interpretation thereof.


 


8.8 Amendments. This Agreement may be amended
by the parties hereto without the consent of any registered holder for the purpose of curing any ambiguity, or of curing, correcting
or supplementing any defective provision contained herein or adding or changing any other provisions, including the shortening
of the Exercise Period pursuant to Section 3.2, with respect to matters or questions arising under this Agreement as the parties
may deem necessary or desirable and that the parties deem shall not adversely affect the interest of the registered holders. All
other modifications or amendments, including any amendment to increase the Warrant Price, shall require the written consent of
a majority of the then outstanding Warrants. Notwithstanding the foregoing, the Company may lower the Warrant Price or extend or
reduce the duration of the Exercise Period in accordance with Sections 3.1 and 3.2, respectively, without such consent.


 


8.9 Severability. This Agreement shall be deemed
severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability
of this Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision,
the parties hereto intend that there shall be added as a part of this Agreement a provision as similar in terms to such invalid
or unenforceable provision as may be possible and be valid and enforceable.


 






    	 	9	 



     


    

 


IN WITNESS WHEREOF, this Agreement has been duly executed by
the parties hereto effective as of the day and year first above written.


 





	ZION OIL & GAS, INC.	 
	 	 
	By:	/s/ Martin M. van Brauman	 
	Name:	Martin M. van Brauman	 
	Title:	Corporate Secretary, Treasurer, SVP, Director	 
	 	 	 
	Date:	April 2, 2018	 
	 	 	 
	AMERICAN STOCK TRANSFER & TRUST COMPANY, LLC	 
	 	 
	By:	/s/ Paula Caroppoli	 
	Name:	Paula Caroppoli	 
	Title:	Senior Vice President	 
	 	 	 
	Date:	April 2, 2018	 







 






    	 	10	 



     


    

 


Exhibit A


 


[Face of Certificate - ZION OIL &
GAS, INC.]


 


(SEE REVERSE SIDE FOR LEGEND)


 


W


 


WARRANTS


 


(THIS WARRANT WILL BE VOID IF NOT EXERCISED
PRIOR TO 5:00 P.M., EASTERN STANDARD TIME, June 29, 2019)


 


ZION OIL & GAS, INC.


 


CUSIP 989696 232


 


WARRANT


 


THIS CERTIFIES THAT, for value received _____________ is the
registered holder of a Warrant or Warrants expiring June 29, 2019 (the “Warrant”) to purchase for each Warrant one fully
paid and non-assessable share of Common Stock, par value $.01 per share (the “Shares”), of ZION OIL & GAS, INC.,
a Delaware corporation (the “Company”). Each Warrant entitles the holder thereof to purchase from the Company, commencing
on June 29, 2018, one Share of the Company at the price of $3.00 per share, upon surrender of this Warrant Certificate and payment
of the Warrant Price at the office or agency of the Warrant Agent, American Stock Transfer & Trust Company, LLC (such surrender
may be made by electronic means and such payment by check or by electronic means made payable to the order of the Company), but
only subject to the conditions set forth herein and in the Warrant Agent Agreement between the Company and the Warrant Agent. In
no event shall the registered holder of this Warrant be entitled to receive a net-cash settlement or other consideration in lieu
of physical settlement in Shares of the Company. The Warrant Agent Agreement provides that, upon the occurrence of certain events,
the Warrant Price, the Exercise Period and the number of Warrant Shares purchasable hereunder, set forth on the face hereof, may,
subject to certain conditions, be adjusted. The term Warrant Price as used in this Warrant Certificate refers to the price per
Share at which Shares may be purchased at the time the Warrant is exercised.


 


This Warrant may expire on the date first above written, if
it is not exercised prior to such date by the registered holder pursuant to the terms of the Warrant Agent Agreement. The Company
in its sole discretion may extend the duration of the Unit Option under the Unit Program, which would extend the Warrant Exercise
Period by the same extension of days.


 


Upon any exercise of the Warrant for less
than the total number of full Shares provided for herein, there shall be issued to the registered holder hereof or his/her/its
assignee a new Warrant Certificate covering the number of Shares for which the Warrant has not been exercised.


 


Warrant Certificates, when surrendered at the office or agency
of the Warrant Agent or by any electronic means to the Company by the registered holder hereof in person or by attorney duly authorized
in writing, may be exchanged in the manner and subject to the limitations provided in the Warrant Agent Agreement, but without
payment of any service charge, for another Warrant Certificate or Warrant Certificates of like tenor and evidencing in the aggregate
a like number of Warrants.


 


Upon due presentment by electronic means
or other approved delivery for registration of transfer of the Warrant Certificate at the office or agency of the Warrant Agent,
a new Warrant Certificate or Warrant Certificates of like tenor and evidencing in the aggregate a like number of Warrants shall
be issued to the transferee in exchange for this Warrant Certificate, subject to the limitations provided in the Warrant Agent
Agreement, without charge except for any applicable tax or other governmental charge.


 


The Company and the Warrant Agent may deem
and treat the registered holder as the absolute owner of the Warrants represented by this Warrant Certificate (notwithstanding
any notation of ownership or other writing hereon made by anyone) for the purpose of any exercise hereof, of any distribution to
the registered holder, and for all other purposes, and neither the Company nor the Warrant Agent shall be affected by any notice
to the contrary.


 






    	 	11	 



     


    

 


This Warrant does not entitle the registered holder to any of
the rights of a stockholder of the Company.


  


COUNTERSIGNED:


American Stock Transfer & Trust Company,
LLC


 


WARRANT AGENT


BY:


AUTHORIZED OFFICER


 


DATED:


 


(Signature)


CHIEF EXECUTIVE OFFICER


 


(Seal)


 


(Signature)


SECRETARY


  








    	 	12