Document:

Exhibit
4.11

 

Annex
B

 

[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, August 6, 2021)

 

ZION
OIL & GAS, INC.

 

CUSIP
989696 265

 

WARRANT

 

THIS
CERTIFIES THAT, for value received _____________ is the registered holder of a Warrant or Warrants expiring August 6, 2021 (the
“Warrant”) to purchase 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”). The Warrant entitles the holder thereof to purchase
from the Company, commencing on August 6, 2019, one Share of the Company at the price of $2.00 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 payment to be made by check made payable to the order of the Company), but only subject to the conditions
set forth herein and in the Warrant 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 Agreement provides that, upon the occurrence of certain events, the Warrant Price 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 Agreement.

 

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 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 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 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 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.

  

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)

SECRETARYExhibit 4.12

 

WARRANT
AGENT AGREEMENT

 

This
Warrant Agent Agreement (this “Agreement”) is made effective as of April 23, 2019, 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 February 1, 2018 amendment to the Warrant Agent Agreement,
to the April 2, 2018 amendment to the Warrant Agreement, to the August 21, 2018 amendment to the Warrant Agreement and to the
December 7, 2018 amendment to the Warrant Agent Agreement by the expansion of the Unit option program. 

 

WHEREAS,
the Company has implemented a Dividend Reinvestment and Common Stock Purchase Plan (hereinafter “DSPP”)
and AST is administering the DSPP as the Plan agent (the “Plan Agent”) and Warrant agent (the “Warrant
Agent”), effective August 1, 2014, (1) under a Warrant Agreement dated August 1, 2014 that is still in effect for
the $2.50 Unit option program and as the continuation of AST as the Warrant Agent under the DSPP for the Warrant ZNWAA, (2) under
a Warrant Agent Agreement dated February 2, 2015 that is still in effect for the $4.00 Unit option program for the Warrant ZNWAD,
(3) under a Warrant Agent Agreement dated November 1, 2016 that is still in effect for the $10.00 Unit option program for the
Warrant ZNWAE, (4) under a Warrant Agent Agreement dated May 22, 2017 for the Warrant ZNWAF that is still in effect for the $250.00
Unit option program, (5) under a Warrant Agent Agreement dated October 12, 2017 for the Warrant ZNWAG that is still in effect
for the $250.00 Unit option program, (6) under a Warrant Agent Agreement dated February 1, 2018 for the Warrant ZNWAH, (7) under
a Warrant Agent Agreement dated April 2, 2018 for the Warrant ZNWAI, (8) under a Warrant Agent Agreement dated August 21, 2018
for the Warrant ZNWAJ, (9) under a Warrant Agent Agreement dated December 7, 2018 for the Warrant ZNWAK and (10) as the continuation
of AST as the Warrant Agent under the DSPP for the Warrant ZNWAL dated April 23, 2019;

 

WHEREAS,
pursuant to the DSPP, the Company is offering a new unit option program consisting of a new Unit (each a “Unit”
and collectively the “Units”) of its securities to existing stockholders and investors, with each Unit
(priced at $250.00 each) is comprised of (i) a certain number of shares of Common Stock determined by dividing $250.00 (the price
of one Unit) by the average of the high and low sale prices of the Company’s publicly traded common stock as reported on
the NASDAQ on the Unit Purchase Date and (ii) Common Stock purchase warrants to purchase an additional fifty (50) shares of Common
Stock at a per share exercise price of $2.00. The Unit Option begins on April 24, 2019 and is scheduled to terminate on June 6,
2019 (unless extended at the Company’s sole discretion). The participant’s Plan account will be credited with the
number of shares of the Company’s Common Stock and warrants that are acquired under the Units purchased. Each warrant affords
the investor the opportunity to purchase one share of our Common Stock at an exercise price of $2.00 per share (each “Warrant”
and collectively the “Warrants”) and each Unit may be purchased at a per Unit price of $250.00;

 

WHEREAS,
for Plan participants who enroll into the Unit Program with the purchase of at least one Unit and also enroll in the separate
Automatic Monthly Investments (“AMI”) program at a minimum of $50.00 per month or more, will receive an additional
twenty-five (25) Warrants at an exercise price of $2.00 during this Unit Option Program. The twenty-five (25) additional warrants
are for enrolling into the AMI program. Existing subscribers to the AMI are entitled to the additional twenty-five (25) warrants
once, if they purchase at least one (1) Unit during the Unit program.

 

     

     

    

 

WHEREAS,
the new Warrants will be exercisable on August 6, 2019, which is the first trading day after the 60th day following
the Unit Option Termination Date (i.e., on June 6, 2019) (unless extended at the Company’s sole discretion) and continue
to be exercisable for two (2) years after the exercise date at a per share exercise price of $2.00 for Warrant as notated by the
Company as ZNWAL; 

 

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 Amendment No. 6 filed April
23, 2019 to facilitate the trading of the shares of Common Stock included in the new Units and the shares of Common Stock underlying
the Warrants that are included in the Units as well as the Warrants;

 

WHEREAS,
the shares of Common Stock included in the Units are tradable on the NASDAQ under the symbol ZN and, following the closing of
the Unit program, 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

     

    

 

2.2
  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 $2.00 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.

 

3.2
  Duration of Warrants. A Warrant may be exercised only during the period commencing on August 6, 2019, which is the
first trading day after the 60th day following the Unit Option Termination Date (i.e., on June 6, 2019) (unless extended
at the Company’s sole discretion) and continue to be exercisable for two (2) 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

     

    

 

3.3
  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
  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

     

    

 

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
  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.

 

    5

     

    

 

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.

 

5.3
  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

     

    

 

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.

 

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

     

    

 

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.

  

7.4.2
  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.

  

    8

     

    

 

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

 

8.3
  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. 

 

    9

     

    

 

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.

  

    10

     

    

 

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 23, 2019	 
	 	 	 
	AMERICAN STOCK TRANSFER & TRUST COMPANY,LLC	 
	 	  	 
	By:	/s/ Michael Nespoli	   
	Name:	Michael Nespoli	 
	Title:	Executive Director	 
	 	Relationship Management	 
	 	 	 
	Date:	April 23, 2019	 

  

    11

     

    

 

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, August 6, 2021)

 

ZION
OIL & GAS, INC.

 

CUSIP
989696 265

 

WARRANT

 

THIS
CERTIFIES THAT, for value received _____________ is the registered holder of a Warrant or Warrants expiring August 6, 2021 (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 August 6, 2019, one Share of the Company at the price of $2.00
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.

 

    12

     

    

 

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.

 

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

 

 

13

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