Cry from women in party rejected (4)
I believe the answer is:
bawl
'cry' is the definition.
('bawl' can be a synonym of 'cry')
'women in party rejected' is the wordplay.
'women' becomes 'w'.
'in' indicates putting letters inside.
'party' becomes 'lab' (abbreviation for Labour).
'rejected' is a reversal indicator.
'w' put into 'lab' is 'lwab'.
'lwab' in reverse letter order is 'BAWL'.
'from' is the link.
(Other definitions for bawl that I've seen before include "Loudly greet" , "Weep noisily" , "Loud cry" , "What baby does" , "wail of discontent" .)