Can a commercial pilot with MPL , obtain PPL for general aviation in the UAE?
Note: You did not specify a country. I will answer for EASA.

You don't need to obtain a PPL, you may use the MPL (Multi-Crew Pilot Licence) if you fulfill the requirements. From EASA Part-FCL (emphasis mine):


  FCL.405.A MPL — Privileges
  
  (a) The privileges of the holder of an MPL are to act as co-pilot in an aeroplane required to be operated
  with a co-pilot.
  
  (b) The holder of an MPL may obtain the extra privileges of:
  
  (1) the holder of a PPL(A), provided that the requirements for the PPL(A) specified in Subpart C are met;
  
  (2) a CPL(A), provided that the requirements specified in FCL.325.A are met.
  
  (c) The holder of an MPL shall have the privileges of his/her IR(A) limited to aeroplanes required to be
  operated with a co-pilot. The privileges of the IR(A) may be extended to single-pilot operations in
  aeroplanes, provided that the licence holder has completed the training necessary to act as PIC in
  single-pilot operations exercised solely by reference to instruments and passed the skill test of the
  IR(A) as a single-pilot.


You can find the requirements of Subpart C in the same PDF on page 145f.