For example, accepting women’s influence (4)
I believe the answer is:
sway
'influence' is the definition.
(swaying is a kind of influencing)
'for example accepting women's' is the wordplay.
'for example' becomes 'say' ('say' can be used to introduce an example).
'accepting' is an insertion indicator (inserted letters are accepted).
'women' becomes 'w' (standard abbreviation).
'say' enclosing 'w' is 'SWAY'.
(Other definitions for sway that I've seen before include "Swing - lean - persuade" , "Rock to and fro" , "Influence; dominance" , "Swing from side to side, or influence opinion" , "Rule; move to and fro" .)