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 "Behave obsequiously like young deer", "Be servile", "Beige", "Light brown colour", "Be obsequious towards young deer?", "Try to gain favour by flattery", "Young fallow deer", "Colour of a young deer", "Grovel" and "Be obsequious, grovel".)