On request, agree to hold an animal (4)
I believe the answer is:
stag
'an animal' is the definition.
(stag is a kind of animal)
'on request agree to hold' is the wordplay.
'to hold' indicates a hidden word (I've seen 'holds' mean this).
'STAG' can be found hidden inside 'on request agree'.
(Other definitions for stag that I've seen before include "Male-only" , "Male animal" , "without female escort" , "Animal - for men only" , "This party is for men only" .)