Tree or horse out West (5)
I believe the answer is:
rowan
'tree' is the definition.
(type of tree)
'horse out west' is the wordplay.
'horse' becomes 'roan' (roan is a kind of horse).
'out' means one lot of letters goes inside another.
'west' becomes 'W' (abbreviation).
'roan' placed around 'w' is 'ROWAN'.
'or' is the link.
(Other definitions for rowan that I've seen before include "Mr Atkinson, actor" , "Mountain-ash" , "Sort of ash" , "-- Williams, theologian" , "Tree bearing bright red berries" .)