Animal enthusiast out West (4)
I believe the answer is:
fawn
'animal' is the definition.
'enthusiast out west' is the wordplay.
'enthusiast' becomes 'fan' (fan is a kind of enthusiast).
'out' indicates putting letters inside.
'west' becomes 'w' ('W' can be a synonym of 'west').
'fan' enclosing 'w' is 'FAWN'.
(Other definitions for fawn that I've seen before include "Try to please" , "Light brown colour" , "Young deer - beige colour" , "Behave obsequiously like young deer" , "Sandy" .)