Animal enthusiast out West (4)
I believe the answer is:
Here is my best explanation:
'animal' is the definition.
'enthusiast out west' is the subsidiary indication.
'enthusiast' becomes 'fan' (fan is a kind of enthusiast).
'out' means one lot of letters goes inside another.
'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 "Be servile", "Pale brown", "Cringe", "Sandy", "Yellowish brown; grovel", "Light brown colour", "Be obsequious, grovel", "Try to gain favour by flattery", "Beige" and "Colour of a young deer".)