Hesitate banning women's claim (4)
I believe the answer is:
aver
'claim' is the definition.
(aver means to state or claim something)
'hesitate banning women's' is the wordplay.
'hesitate' becomes 'waver' (wavering is a kind of hesitating).
'banning' suggests deleting specific letters.
'women' becomes 'w' (standard abbreviation).
'waver' with 'w' taken out is 'AVER'.
(Other definitions for aver that I've seen before include "State firmly, maybe rave" , "Declare or insist" , "State; say" , "State firmly - even rave about" , "possessions once" .)