Animal's leg cut (4)
I believe the answer is:
stag
'animal's' is the definition.
(stag is a kind of animal)
'leg cut' is the wordplay.
'leg' becomes 'stage' ('stage' can be a synonym of 'leg').
'cut' means to remove the last letter.
'stage' with its last letter taken off is 'STAG'.
(Other definitions for stag that I've seen before include "No women allowed" , "Men-only" , "Hunted animal" , "This party is for men only" , "Antlered beast" .)