tst> connect system/manager@tst
Connected.
tst> grant create any context to u1;

Grant succeeded.

tst> connect u1/u1@tst
Connected.
tst> create package pkg1 as
   2   procedure assign(name varchar2, value varchar2);
   3   end;
   4   /

Package created.

tst> create package body pkg1 as
   2   procedure assign(name varchar2, value varchar2) is
   3   begin
   4   dbms_session.set_context('CTX', name, value);
   5   end;
   6   end;
   7   /

Package body created.

tst> create package pkg2 as
   2   procedure assign(name varchar2, value varchar2);
   3   end;
   4   /

Package created.

tst> create package body pkg2 as
   2   procedure assign(name varchar2, value varchar2) is
   3   begin
   4   dbms_session.set_context('CTX', name, value);
   5   end;
   6   end;
   7   /

Package body created.

tst> create context ctx using pkg2;  -- Доверенный пакет pkg2 

Context created.

tst> exec pkg2.assign('2', '22');

PL/SQL procedure successfully completed.

tst> exec pkg1.assign('1', '11');
BEGIN pkg1.assign('1', '11'); END;

*
ERROR at line  1 :
ORA- 01031 : insufficient privileges
ORA- 06512 : at "SYS.DBMS_SESSION", line  78 
ORA- 06512 : at "U1.PKG1", line  4 
ORA- 06512 : at line  1 


tst> select namespace, attribute, substr(value,  1 ,  10 ) from session_context;

NAMESPACE                      ATTRIBUTE                      SUBSTR(VAL
 ------------------------------ ------------------------------ ---------- 
CTX                             2                                22