Possibly retaining western influence (4)
I believe the answer is:
sway
'possibly retaining western influence' is the definition.
'sway' can be an answer for 'influence' (I've seen this before). I am unsure of the 'possibly retaining western' bit.
'retaining western influence' is the wordplay.
'retaining' is an insertion indicator (inserted letters are held or retained).
'western' becomes 'w'.
'influence' becomes 'say' (I've seen this in another clue).
'w' put into 'say' is 'SWAY'.
Can you help me to learn more?
(Other definitions for sway that I've seen before include "Strong influence" , "Rock to and fro" , "Bend; influence" , "Totter; influence" , "Move gently" .)