<PAGE>   1
                                                                  EXHIBIT 4.3.13


================================================================================


                   CAPSTAR RADIO BROADCASTING PARTNERS, INC.,
                                   AS ISSUER,

                               THE PARTIES LISTED
                             ON THE SIGNATURE PAGES
                             HERETO AS GUARANTORS,
                                 AS GUARANTORS,

                                      AND

                 IBJ SCHRODER BANK & TRUST COMPANY, AS TRUSTEE

                          ---------------------------

                                AMENDMENT NO. 12

                         DATED AS OF DECEMBER 15, 1997

                                     TO THE

                                   INDENTURE

                           DATED AS OF APRIL 21, 1995

                          ---------------------------

                                  $76,808,000

                   13 1/4% SENIOR SUBORDINATED NOTES DUE 2003

================================================================================
<PAGE>   2
         AMENDMENT NO. 12, dated as of December 15, 1997 ("Amendment No. 12"),
to the INDENTURE, dated as of April 21, 1995, as amended (the "Indenture"),
among CAPSTAR RADIO BROADCASTING PARTNERS, INC., a Delaware corporation, as
Issuer (the "Company"), the parties listed on the signature pages hereto as
Guarantors (each individually, a "Guarantor" and collectively, the
"Guarantors"), and IBJ SCHRODER BANK & TRUST COMPANY, a New York banking
corporation, as Trustee (the "Trustee").

         Each party agrees for the benefit of the other parties and for the
equal and ratable benefit of the Holders of the Company's 13 1/4% Senior
Subordinated Notes due 2003 (the "Notes") to amend, pursuant to Section 8.01(4)
of the Indenture, the Indenture as follows:

         1.      K-106, Inc., a Texas corporation ("K-106"), is a wholly-owned
indirect subsidiary of the Company, and is a Restricted Subsidiary acquired or
created pursuant to Section 4.14(ii) of the Indenture.  K-106 delivers herewith
the Guarantee attached as Exhibit A to this Amendment No. 12 pursuant to the
provisions set forth in Sections 4.14 and 10.04 of the Indenture guaranteeing
the obligations of the Company under the Indenture.  For all purposes of the
Indenture, K-106 shall be deemed a party to the Indenture by virtue of its
execution of this Amendment No. 12 and the defined term "Guarantor" contained
in Article 1.01 of the Indenture shall be deemed to include K-106.

         2.      GulfStar Beaumont Broadcasting, Inc., a Texas corporation
("GulfStar Beaumont"), is a wholly-owned indirect subsidiary of the Company,
and is a Restricted Subsidiary acquired or created pursuant to Section 4.14(ii)
of the Indenture.  GulfStar Beaumont delivers herewith the Guarantee attached
as Exhibit A to this Amendment No. 12 pursuant to the provisions set forth in
Sections 4.14 and 10.04 of the Indenture guaranteeing the obligations of the
Company under the Indenture.  For all purposes of the Indenture, GulfStar
Beaumont shall be deemed a party to the Indenture by virtue of its execution of
this Amendment No. 12 and the defined term "Guarantor" contained in Article
1.01 of the Indenture shall be deemed to include GulfStar Beaumont.

         3.      This Amendment No. 12 supplements the Indenture and shall be a
part and subject to all the terms thereof.  Except as supplemented hereby, the
Indenture and the Securities issued thereunder shall continue in full force and
effect.

         4.      This Amendment No. 12 may be executed in counterparts, each of
which shall be deemed an original, but all of which shall together constitute
one and the same instrument.

         5.      THIS AMENDMENT NO. 12 SHALL BE GOVERNED BY, AND CONSTRUED IN
ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK (WITHOUT GIVING EFFECT TO
THE CONFLICT OF LAWS PRINCIPLES THEREOF THAT WOULD RESULT IN THE APPLICATION OF
THE LAWS OF ANOTHER JURISDICTION).

         6.      The Trustee shall not be responsible for any recital herein as
such recitals shall be taken as statements of the Company, or the validity of
the execution by the Guarantor of the Amendment No. 12.  The Trustee makes no
representation as to the validity or sufficiency of this Amendment No. 12.



                                     -1-
<PAGE>   3
         IN WITNESS WHEREOF, the parties have caused this Amendment  No. 12 to
the Indenture to be duly executed and attested as of the date and year first
written above.

                                       CAPSTAR RADIO BROADCASTING PARTNERS, INC.



                                        By: /s/ WILLIAM S. BANOWSKY, JR.
                                           -------------------------------------
                                           William S. Banowsky, Jr.  
                                           Executive Vice President

ATTEST:


---------------------------
Kathy Archer
Assistant Secretary

                                   GUARANTORS:

                                   AMERON BROADCASTING CORPORATION
                                   ASHEVILLE BROADCASTING CORP.
                                   ATLANTIC STAR COMMUNICATIONS, INC.
                                   ATLANTIC CITY BROADCASTING CORP.
                                   BATON ROUGE BROADCASTING COMPANY, INC.
                                   BC FUNDS HOLDINGS CO., INC.
                                   BEATRICE BROADCASTING CORP.
                                   BENCHMARK COMMUNICATIONS HOLDINGS, INC.
                                   BREADBASKET BROADCASTING CORPORATION
                                   CAPSTAR ACQUISITION COMPANY, INC.
                                   CENTRAL STAR COMMUNICATIONS, INC.
                                   COMMODORE MEDIA OF KENTUCKY, INC.
                                   COMMODORE MEDIA OF NORWALK, INC.
                                   COMMODORE MEDIA FLORIDA, INC.
                                   COMMODORE MEDIA OF WESTCHESTER, INC.
                                   COMMODORE MEDIA OF PENNSYLVANIA, INC.
                                   COMMODORE MEDIA OF DELAWARE, INC
                                   CONGAREE BROADCASTERS, INC.
                                   CORKSCREW BROADCASTING CORPORATION
                                   COUNTRY HEARTLINES, INC.
                                   CURREY BROADCASTING CORPORATION
                                   DANBURY BROADCASTING, INC
                                   DAYTONA BEACH BROADCASTING CORP.
                                   DIXIE BROADCASTING, INC.
                                   GREAT AMERICAN EAST, INC.
                                   GULFSTAR COMMUNICATIONS WACO LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS PORT ARTHUR
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS CORPUS CHRISTI
                                           LICENSEE, INC.
                                  
                                  
                                  
                                  
                                  
                                  
<PAGE>   4
                                   GULFSTAR BEAUMONT BROADCASTING, INC.
                                   GULFSTAR COMMUNICATIONS BEAUMONT 
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS LUFKIN LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS BATON ROUGE
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS VICTORIA 
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS OKLAHOMA 
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS OKLAHOMA, INC.
                                   GULFSTAR COMMUNICATIONS LUBBOCK 
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS TYLER LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS KILLEEN 
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS, INC.
                                   GULFSTAR COMMUNICATIONS HOLDINGS, INC.
                                   GULFSTAR COMMUNICATIONS MANAGEMENT, INC.
                                   GULFSTAR COMMUNICATIONS BEAUMONT, INC.
                                   GULFSTAR COMMUNICATIONS LUFKIN, INC.
                                   GULFSTAR COMMUNICATIONS PORT ARTHUR, INC.
                                   GULFSTAR COMMUNICATIONS TEXARKANA, INC.
                                   GULFSTAR COMMUNICATIONS TYLER, INC.
                                   GULFSTAR COMMUNICATIONS VICTORIA, INC.
                                   GULFSTAR COMMUNICATIONS BATON ROUGE, INC.
                                   GULFSTAR COMMUNICATIONS NEW MEXICO 
                                           LICENSEE, INC.
                                   GULFSTAR COMMUNICATIONS CORPUS CHRISTI, INC.
                                   GULFSTAR COMMUNICATIONS WACO, INC.
                                   GULFSTAR COMMUNICATIONS ARKANSAS, INC.
                                   GULFSTAR COMMUNICATIONS NEW MEXICO, INC.
                                   GULFSTAR COMMUNICATIONS KILLEEN, INC.
                                   GULFSTAR COMMUNICATIONS LUBBOCK, INC.
                                   GULFSTAR COMMUNICATIONS ARKANSAS 
                                           LICENSEE, INC.       
                                   GULFSTAR COMMUNICATIONS TEXARKANA
                                           LICENSEE, INC.
                                   HOUNDSTOOTH BROADCASTING CORPORATION
                                   JAMBOREE IN THE HILLS, INC
                                   K-106, INC.
                                   LADNER COMMUNICATIONS HOLDING CORP.
                                   MOUNTAIN RADIO CORPORATION
                                   NELSON BROADCASTING CORPORATION
                                   O.C.C., INC.
                                   ORANGE COMMUNICATIONS, INC.
                                   OSBORN SOUND & COMMUNICATIONS CORP.
                                   OSBORN ENTERTAINMENT ENTERPRISES CORPORATION
                                   PACIFIC STAR COMMUNICATIONS, INC.
                                   RADIO WBHP, INC.
                                   RADIOCO I, INC.
                                   RADIOCO II, INC.
                                   RAINBOW BROADCASTING CORPORATION
                                   RKZ TELEVISION, INC.
                                   SHORT BROADCASTING CORPORATION
                                  
                                  
                                  
                                  
                                  
                                  
<PAGE>   5
                                   SNG HOLDINGS, INC.
                                   SONANCE WACO LICENSE SUBSIDIARY, INC.
                                   SONANCE WACO OPERATING COMPANY, INC.
                                   SOUTHEAST RADIO HOLDING CORP.
                                   SOUTHERN STAR COMMUNICATIONS, INC.
                                   WAITE BROADCASTING CORP.
                                   WNOK ACQUISITION COMPANY, INC.
                                   YELLOW BRICK RADIO CORPORATION
                                  
                                  
                                  
                                   By: /s/ WILLIAM S. BANOWSKY, JR.
                                       -----------------------------------------
                                         William S. Banowsky, Jr.
                                         Vice President
                                  
ATTEST:                           
                                  
/s/ KATHY ARCHER                                  
--------------------------------                                  
Kathy Archer                      
Assistant Secretary               
                                  
                                  
                                  
                                  
                                  
                                  
<PAGE>   6
                                  MOUNTAIN LAKES BROADCASTING, L.L.C.

                                  By:     Dixie Broadcasting, Inc.,
                                          its Member


                                          By: /s/ WILLIAM S. BANOWSKY, JR.
                                              ----------------------------------
                                              William S. Banowsky, Jr.
                                              Vice President

ATTEST:

/s/ KATHY ARCHER
---------------------------------
Kathy Archer
Assistant Secretary

                                  By:     Radio WBHP, Inc.,
                                          its Member


                                          By: /s/ WILLIAM S. BANOWSKY, JR. 
                                              ----------------------------------
                                              William S. Banowsky, Jr.
                                              Vice President
ATTEST:

/s/ KATHY ARCHER
----------------------------------
Kathy Archer
Assistant Secretary


                                  WILMINGTON WJBR-FM, L.L.C.

                                  By:     Commodore Media of Delaware, Inc.,
                                          its Manager


                                          By: /s/ WILLIAM S. BANOWSKY, JR.
                                              ----------------------------------
                                              William S. Banowsky, Jr.
                                              Vice President

ATTEST:

/s/ KATHY ARCHER
----------------------------------
Kathy Archer
Assistant Secretary






<PAGE>   7
                                   MUSIC HALL CLUB, INC.


                                  By: /s/ LARRY ANDERSON
                                      ------------------------------------------
                                      Larry Anderson
                                      President
ATTEST:

/s/ NANCY ANDERSON
-----------------------------------
Nancy Anderson
Secretary and Treasurer






<PAGE>   8
                                  BENCHMARK COMMUNICATIONS RADIO LIMITED
                                       PARTNERSHIP

                                  By:     Benchmark Communications Holdings, 
                                          Inc., its General Partner



                                  By: /s/ WILLIAM S. BANOWSKY, JR.
                                      ------------------------------------------
                                      William S. Banowsky, Jr.  
                                      Vice President

ATTEST


/s/ KATHY ARCHER
-----------------------------------
Kathy Archer
Assistant Secretary


                                   BENCHMARK JACKSON, L.L.C.

                                   By:     Benchmark Communications Radio
                                           Limited Partnership, its
                                           Member

                                   By:     Benchmark Communications
                                           Holdings, Inc., its General
                                           Partner



                                   By: /s/ WILLIAM S. BANOWSKY, JR.
                                       -----------------------------------------
                                       William S. Banowsky, Jr.  
                                       Vice President

ATTEST


/s/ KATHY ARCHER
-----------------------------------
Kathy Archer
Assistant Secretary





<PAGE>   9
                                   BENCHMARK RADIO ACQUISITION FUND I LIMITED
                                           PARTNERSHIP
                                   BENCHMARK RADIO ACQUISITION FUND IV LIMITED
                                           PARTNERSHIP
                                   BENCHMARK RADIO ACQUISITION FUND VII LIMITED
                                           PARTNERSHIP
                                   BENCHMARK RADIO ACQUISITION FUND VIII LIMITED
                                           PARTNERSHIP
                                   BENCHMARK RADIO ACQUISITION FUND IX LIMITED
                                           PARTNERSHIP
                                   BENCHMARK RADIO ACQUISITION FUND XI LIMITED
                                           PARTNERSHIP
                                   
                                   By:     Benchmark Communications Radio 
                                           Limited Partnership, its General 
                                           Partner
                                   
                                   By:     Benchmark Communications Holdings, 
                                           Inc., its General Partner
                                   
                                   
                                   By: /s/ WILLIAM S. BANOWSKY, JR.
                                       ----------------------------------------
                                       William S. Banowsky, Jr.
                                       Vice President
                                   
ATTEST


/s/ KATHY ARCHER
-----------------------------------
Kathy Archer
Assistant Secretary



<PAGE>   10
                                   WDOV LICENSE LIMITED PARTNERSHIP 
                                   WDSD LICENSE LIMITED PARTNERSHIP 
                                   WSRV LICENSE LIMITED PARTNERSHIP
                                   
                                   By:     Benchmark Radio Acquisition
                                           Fund I Limited Partnership,
                                           its General Partner
                                   
                                   By:     Benchmark Communications Radio
                                           Limited Partnership, its
                                           General Partner
                                   
                                   By:     Benchmark Communications
                                           Holdings, Inc., its General
                                           Partner
                                   
                                   
                                   
                                   By: /s/ WILLIAM S. BANOWSKY, JR.
                                       ----------------------------------------
                                       William S. Banowsky, Jr.  
                                       Vice President
                                   
ATTEST                             
                                   
                                   
/s/ KATHY ARCHER
---------------------------------
Kathy Archer
Assistant Secretary






<PAGE>   11
                                   BENCHMARK RADIO ACQUISITION FUND V
                                             LIMITED PARTNERSHIP
                                   WOSC LICENSE LIMITED PARTNERSHIP 
                                   WKOC LICENSE LIMITED PARTNERSHIP 
                                   WWFG LICENSE LIMITED PARTNERSHIP
                                   
                                   By:     Benchmark Radio Acquisition
                                           Fund IV Limited Partnership,
                                           its General Partner
                                   
                                   By:     Benchmark Communications Radio
                                           Limited Partnership, its
                                           General Partner
                                   
                                   By:     Benchmark Communications
                                           Holdings, Inc., its General
                                           Partner
                                   
                                   
                                   
                                   By: /s/ WILLIAM S. BANOWSKY, JR.
                                      ------------------------------------------
                                      William S. Banowsky, Jr.  
                                      Vice President
                                   
ATTEST                             


/s/ KATHY ARCHER
-----------------------------------
Kathy Archer
Assistant Secretary





                                   
<PAGE>   12
                                   WCOS (AM) LICENSE LIMITED PARTNERSHIP
                                   WCOS-FM LICENSE LIMITED PARTNERSHIP
                                   WHKZ LICENSE LIMITED PARTNERSHIP
                                   WVOC LICENSE LIMITED PARTNERSHIP
                                   
                                   By:     Benchmark Radio Acquisition
                                           Fund V Limited Partnership,
                                           its General Partner
                                   
                                   By:     Benchmark Radio Acquisition
                                           Fund IV Limited Partnership,
                                           its General Partner
                                   
                                   By:     Benchmark Communications Radio
                                           Limited Partnership, its
                                           General Partner
                                   
                                   By:     Benchmark Communications
                                           Holdings, Inc., its General
                                           Partner
                                   
                                   
                                   
                                   By: /s/ WILLIAM S. BANOWSKY, JR.
                                      ------------------------------------------
                                        William S. Banowsky, Jr.  
                                        Vice President
                                   
ATTEST


/s/ KATHY ARCHER
-----------------------------------
Kathy Archer
Assistant Secretary





                                   
<PAGE>   13
                                   WJMZ LICENSE LIMITED PARTNERSHIP

                                   By:     Benchmark Radio Acquisition
                                           Fund VII Limited Partnership,
                                           its General Partner

                                   By:     Benchmark Communications Radio
                                           Limited Partnership, its
                                           General Partner
                                   
                                   By:     Benchmark Communications
                                           Holdings, Inc., its General
                                           Partner
                                   
                                   
                                   
                                   By: /s/ WILLIAM S. BANOWSKY, JR.
                                      ------------------------------------------
                                        William S. Banowsky, Jr.  
                                        Vice President
                                   
ATTEST                             
                                   
                                   
/s/ KATHY ARCHER                                   
-----------------------------------                                   
Kathy Archer                       
Assistant Secretary                
                                   
                                  BENCHMARK GREENVILLE, L.L.C.
                                   
                                  By:     Benchmark Radio Acquisition Fund III 
                                          Limited Partnership, its Manager

                                  By:     Benchmark Communications Radio
                                          Limited Partnership, its
                                          General Partner
                                  
                                  By:     Benchmark Communications
                                          Holdings, Inc., its General
                                          Partner
                                  
                                  
                                  
                                  By: /s/ WILLIAM S. BANOWSKY, JR.
                                     ------------------------------------------
                                        William S. Banowsky, Jr.  
                                        Vice President
                                  
ATTEST                            
                                  
                                  
/s/ KATHY ARCHER                                  
----------------------------------                                  
Kathy Archer                      
Assistant Secretary               
                                  
                                  
                                  
                                  
                                  
                                  
<PAGE>   14
                                  WESC(AM) LICENSE LIMITED PARTNERSHIP
                                  WESC-FM LICENSE LIMITED PARTNERSHIP
                                  WFNQ LICENSE LIMITED PARTNERSHIP
                                  
                                  By:     Benchmark Greenville, L.L.C.,
                                          its General Partner
                                  
                                  By:     Benchmark Radio Acquisition
                                          Fund VII Limited Partnership,
                                          its Member
                                  
                                  By:     Benchmark Communications Radio
                                          Limited Partnership, its
                                          General Partner
                                  
                                  By:     Benchmark Communications
                                          Holdings, Inc., its General
                                          Partner
                                  
                                  
                                  
                                  By: /s/ WILLIAM S. BANOWSKY, JR.
                                     ------------------------------------------
                                        William S. Banowsky, Jr.  
                                        Vice President
                                  
ATTEST                            
                                  
                                  
/s/ KATHY ARCHER                                  
---------------------------------                                  
Kathy Archer                      
Assistant Secretary               
                                  
                                  
                                  
                                  


<PAGE>   15
                                  WUSQ LICENSE LIMITED PARTNERSHIP 
                                  WNTW LICENSE LIMITED PARTNERSHIP 
                                  WYYD LICENSE LIMITED PARTNERSHIP 
                                  WROV(AM) LICENSE LIMITED PARTNERSHIP 
                                  WROV-FM LICENSE LIMITED PARTNERSHIP
                                  
                                  By:     Benchmark Radio Acquisition
                                          Fund VIII Limited
                                          Partnership, its General
                                          Partner
                                  
                                  By:     Benchmark Communications Radio
                                          Limited Partnership, its
                                          General Partner
                                  
                                  By:     Benchmark Communications
                                          Holdings, Inc., its General
                                          Partner
                                  
                                  
                                  
                                  By: /s/ WILLIAM S. BANOWSKY, JR.
                                     ------------------------------------------
                                        William S. Banowsky, Jr.  
                                        Vice President
ATTEST:                           
                                  
/s/ KATHY ARCHER                                  
----------------------------------                                  
Kathy Archer                      
Assistant Secretary               
                                  
                                  BENCHMARK RADIO ACQUISITION FUND VI, LC
                                  
                                  By:     Benchmark Radio Acquisition Fund VIII
                                          Limited Partnership, its Member

                                  By:     Benchmark Communications Radio
                                          Limited Partnership, its
                                          General Partner

                                  By:     Benchmark Communications
                                          Holdings, Inc., its General
                                          Partner



                                  By: /s/ WILLIAM S. BANOWSKY, JR.
                                     ------------------------------------------
                                        William S. Banowsky, Jr.  
                                        Vice President
ATTEST:

/s/ KATHY ARCHER
----------------------------------
Kathy Archer
Assistant Secretary





                                  
<PAGE>   16
                                  IBJ SCHRODER BANK & TRUST COMPANY, as
                                  Trustee



                                  By:   
                                        ----------------------------------------
                                  Name:
                                        ----------------------------------------
                                  Title:
                                        ----------------------------------------
                                  
ATTEST:                           
                                  
                                  
                                  
----------------------------------------
Name:
     -----------------------------------
Title:                            
     -----------------------------------





<PAGE>   17
                                   EXHIBIT A

                                   GUARANTEE

         The Guarantors (the "Guarantors," which term includes any successor
Person under the Indenture, dated  April 21, 1995, as amended, among Capstar
Radio Broadcasting Partners, Inc. and its subsidiaries and IBJ Schroder Bank &
Trust Company (the "Indenture")) have unconditionally guaranteed, on a senior
subordinated basis, to the extent set forth in the Indenture and subject to the
provisions of the Indenture, (a) the due and punctual payment of the principal
of and interest on the Notes, whether at maturity, by acceleration or
otherwise, the due and punctual payment of interest on overdue principal, and,
to the extent permitted by law, interest, and the due and punctual performance
of all other obligations of the Company to the Noteholders or the Trustee all
in accordance with the terms set forth in Article 10 of the Indenture, and (b)
in case of any extension of time of payment or renewal of any Notes or any of
such other obligations, that the same will be promptly paid in full when due or
performed in accordance with the terms of the extension or renewal, whether at
stated maturity, by acceleration or otherwise.

         The obligations of the Guarantors to the Noteholders and to the
Trustee pursuant to this Guarantee and the Indenture are expressly set forth in
Article 10 of the Indenture and reference is hereby made to the Indenture for
the precise terms of this Guarantee.  Terms used and not defined herein shall
have the meaning set forth in the Indenture.

                                        GUARANTORS:

                                        K-106, INC.  
                                        GULFSTAR BEAUMONT BROADCASTING, INC.



                                        By: /s/ WILLIAM S. BANOWSKY, JR.
                                           -------------------------------------
                                                William S. Banowsky, Jr.  
                                                Vice President