Part of theatre largely for men only (4)
I believe the answer is:
stag
'men only' is the definition.
(as in a stag do)
'part of theatre largely' is the wordplay.
'part of theatre' becomes 'stage' ('stage' is part of 'theatre').
'largely' means to remove the last letter (most but not all of the letters).
'stage' with its final letter taken away is 'STAG'.
'for' is the link.
(Other definitions for stag that I've seen before include "one may get in a rut" , "Investor" , "Without women" , "Stock market speculator" , "American party" .)