<PAGE>
 
                                                                EXHIBIT 10.13(a)


                       ________________________________


                                AMENDMENT NO. 1

                                  dated as of

                               November 17, 1997

                                      to

                           AIRCRAFT LEASE AGREEMENT

                           dated as of June 3, 1996

                                    BETWEEN

                            POLARIS HOLDING COMPANY

                                   as Lessor

                                      AND

                            FRONTIER AIRLINES, INC.

                                   as Lessee

                       ________________________________


                       One Boeing Model 737-2L9 Aircraft

                        Manufacturer's Serial No. 22734
                         U.S. Registration No. N271FL
<PAGE>
 
                                AMENDMENT NO. 1
                                      to
                           Aircraft Lease Agreement

     THIS AMENDMENT NO. 1 dated as of November 17, 1997 to the Aircraft Lease
Agreement dated as of June 3, 1996 (the "Lease Agreement") between Polaris
Holding Company ("Lessor"), and Frontier Airlines, Inc. ("Lessee").

     WHEREAS, the Lease Agreement as supplemented by Lease Supplement No. 1
dated June 26, 1996 ("Lease Supplement No. 1") was recorded by the Federal
Aviation Administration (the "FAA") on August 7, 1996, as Conveyance No. X129854
(the Lease Agreement as so supplemented is hereinafter referred to as the
"Lease"):

     WHEREAS, the Lease is in respect of one Boeing Model 737-2L9 Aircraft
bearing manufacturer's serial number 22734 and U.S. Registration No. N271FL, and
certain related equipment (the "Aircraft"), and

     WHEREAS, Lessee and Lessor desire to amend the Lease to extend the Term by
an additional twelve months, and to make certain other changes therein, and

     WHEREAS, capitalized terms used and not otherwise defined herein shall have
the meanings ascribed to them in the Lease.

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

1.   Amendments to the Lease.

     The definition of Expiry Date in Clause 1.1 of the Lease is revised in its
entirety to read:

          EXPIRY DATE:   the day preceding the day which is the 72nd monthly
                         anniversary of the Delivery Date or if earlier the date
                         on which:

                         (a) the date Lessor, acting in accordance with the
                         terms of this Agreement terminates the leasing of the
                         Aircraft to Lessee under this Agreement; or

                         (b) Lessor receives the Agreed Value together with any
                         other amounts then due and unpaid by Lessee following
                         an Event of Loss.



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<PAGE>
 
2.   Ratification.
     ------------ 

     Except as expressly provided herein, Lessee acknowledges that nothing
contained in this Amendment is intended to discharge, amend or otherwise modify
its obligations under the Lease The Lease is hereby ratified and confirmed, but
only as amended, in all respects.

3.   Representations and Warranties of Lessee.
     ---------------------------------------- 

     Lessee represents and warrants to Lessor that:

     (a) Lessee has full corporate power, authority and legal right to own its
property and to carry on its business as now being conducted and is duly
authorized to execute and deliver this Amendment, and to perform its obligations
hereunder and thereunder;

     (b) This Amendment has been duly authorized, executed and delivered by
Lessee and constitutes the legal, valid and binding obligation of Lessee
enforceable in accordance with its terms, except as such enforceability may be
limited by applicable bankruptcy, insolvency, moratorium or other similar laws
affecting creditors' rights generally and subject to principles of equity;

     (c) The execution and delivery by Lessee of this Amendment will not
conflict with or result in any breach of, constitute any default under, or
result in the creation of any lien, charge or encumbrance pursuant to, any
applicable law, any term or provision of Lessee's articles of incorporation or
by-laws or any judgment, order, writ, injunction, or decree of any court,
omission, board or Governmental Entity, or contravene any indenture, mortgage,
credit agreement, lease, license, contract or other agreement to which Lessee is
a party or by which it is bound; and

     (d) All consents or approvals required of Lessee by any Governmental Entity
or other Person in connection with the execution and delivery of this Amendment
and the consummation by Lessee of the transactions contemplated hereby have been
duly obtained or waived.

4.   Representations and Warranties of Lessor.
     ---------------------------------------- 

     Lessor represents and warrants to Lessee that:

     (a) Lessor has full corporate power, authority and legal right to own its
property and to carry on its business as now being conducted and is duly
authorized to execute and deliver this Amendment and to perform its obligations
hereunder;

     (b) this Amendment has been duly authorized, executed and delivered by
Lessor and constitutes the legal, valid and binding obligation of Lessor
enforceable in accordance with its 



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<PAGE>

terms, except as such enforceability may be limited by applicable bankruptcy,
insolvency, moratorium or other similar laws affecting creditors' rights
generally and subject to principles of equity;
 
     (c) The execution and delivery by Lessor of this Amendment will not
conflict with or result in any breach of, constitute any default under, or
result in the creation of any lien, charge or encumbrance pursuant to, any
applicable law, any term or provision of or Lessor's articles of incorporation
or by-laws or any judgment, order, writ, injunction, or decree of any court,
commission, board of Governmental Entity, or contravene any indenture, mortgage,
credit agreement, lease, license, contract or other agreement to which Lessor is
a party or by which it is bound; and

     (d) Any consents or approvals required of Lessor by any Governmental Entity
in connection with the execution and delivery of this Amendment and the
consummation by Lessor of the transactions contemplated hereby have been duly
obtained or waived.

5.   Miscellaneous.
     ------------- 

     (a) Amendment.  No amendment, modification or waiver of any provision of
         ---------                                                           
this Amendment shall in any event be effective unless the same shall be in
writing and signed by the parties hereto or, in the case of a waiver, by the
party waiving compliance, and then such waiver shall be effective only in the
specific instance and for the specific purpose for which given.

     (b) Notices.  Any notices, requests, demands or other communications
         -------                                                         
required or permitted to be made hereunder shall be in writing and shall be
addressed provided in Clause 16 11 of the Lease.

     (c) Governing Law.  THIS AMENDMENT, SHALL IN ALL RESPECTS BE GOVERNED BY,
         -------------                                           
AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF CALIFORNIA.

     (d)  Severability.  If any one or more of the provisions contained in this
          ------------                                                         
Amendment or any document executed in connection herewith shall be invalid,
illegal or unenforceable in any respect under any law, the validity, legality
and enforceability of the remaining provisions contained herein shall not in any
way be affected or impaired.

     (e) Counterparts.  This Amendment may be executed in counterparts and any
         ------------                                                         
single counterpart or set of counterparts signed in either case, by all of the
parties hereto shall for all purposes be deemed to be an original, and all such
counterparts when taken together shall constitute one and the same instrument. A
facsimile signature on any counterpart hereto will be deemed an original for all
purposes.

     (f) Entire Agreement.  The terms and conditions contained in the Lease,
         ----------------                                                   
this


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<PAGE>
 
Amendment and the other documents and instruments executed in connection
therewith or herewith constitute the entire agreement among the parities
pertaining to the subject matter thereof and hereof and supersede all prior
agreements, understandings, negotiations and discussions, whether oral or
written, of the parties.

     (g) Headings.  The headings in this Amendment are for reference only, and
         --------                                                             
do not form part of and are not to be used to interpret this Agreement.

     (h)  Further Assurances.  Each party shall cooperate with the other and
          ------------------                                                
execute and deliver such instruments and other documents as my be necessary to
effectuate and carry out the provisions of this Amendment.

     (i)  Successors and Assigns.  This Amendment shall insure to the benefit
          ----------------------                                             
of, and be binding upon, the parties hereto and their respective successors and
assigns.


     IN WITNESS WHEREOF, the parties hereto have caused this Amendment No. 1 to
be duly executed by their respective officers thereunto duly authorized as of
the day and year first above written.

                                        LESSOR:

                                        POLARIS HOLDING COMPANY

                                        By:   /s/ Henry A. Hubschman
                                           --------------------------------

                                        Name: Henry A. Hubschman
                                             ------------------------------

                                        Title: President
                                              -----------------------------

 
                                        LESSEE:
 
                                        FRONTIER AIRLINES, INC.
 
                                        By:    /s/ William B. Durlin
                                           --------------------------------
 
                                        Name:  William B. Durlin
                                             ------------------------------
 
                                        Title:  Vice President
                                              ----------------------------- 


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