SQL> alter session set nls_date_format='DD/MM/YYYY'
  2  /

Session altered.

SQL> SELECT hire_date original
  2       , CASE WHEN TO_CHAR(hire_date,'MM') <= TO_CHAR(SYSDATE,'MM')
  3         THEN
  4           sysdate
  5         ELSE
  6           hire_date
  7         END my_date
  8    FROM employees
  9  /

ORIGINAL   MY_DATE
---------- ----------
17/06/1987 17/06/1987
21/09/1989 21/09/1989
13/01/1993 28/02/2006
03/01/1990 28/02/2006
21/05/1991 21/05/1991
25/06/1997 25/06/1997
05/02/1998 28/02/2006
07/02/1999 28/02/2006
17/08/1994 17/08/1994
16/08/1994 16/08/1994
28/09/1997 28/09/1997
...<snip>...

SQL> SELECT to_char(hire_date,'MM') original
  2       , GREATEST(to_char(hire_date,'MM')
  3                 ,to_char(SYSDATE,'MM')
  4                 ) my_month
  5    FROM employees
  6  /

OR MY
-- --
06 06
09 09
01 02
01 02
05 05
06 06
02 02
02 02
08 08
08 08
09 09
...<snip> ...