Seek approval from women kept by lover (4)
I believe the answer is:
fawn
'seek approval from' is the definition.
(to fawn is to flatter)
'women kept by lover' is the wordplay.
'women' becomes 'w' (standard abbreviation).
'kept by' is an insertion indicator.
'lover' becomes 'fan' (synonyms).
'w' placed inside 'fan' is 'FAWN'.
(Other definitions for fawn that I've seen before include "Light brown colour" , "shade" , "Try to gain favour by flattery" , "Greyish brown" , "Flatter, be obsequious like young deer" .)