Some animal makes offer outside gym (5)
I believe the answer is:
biped
'some animal' is the definition.
(biped is a kind of animal)
'offer outside gym' is the wordplay.
'offer' becomes 'bid' (bid is a kind of offer).
'outside' means one lot of letters goes inside another.
'gym' becomes 'pe' (short for Physical Education).
'bid' placed around 'pe' is 'BIPED'.
'makes' acts as a link.
(Other definitions for biped that I've seen before include "Primate, for example" , "One walking on two legs" , "Man, perhaps" , "Two-footed animal" , "Man, say" .)