Top position? Not quite for this animal (3)
I believe the answer is:
ape
'this animal' is the definition.
(ape is a kind of animal)
'top position? not quite' is the wordplay.
'top position?' becomes 'apex' (apex means the top or peak).
'not quite' means to remove the last letter (most but not all of the word).
'apex' with its final letter taken off is 'APE'.
'for' acts as a link.
(Other definitions for ape that I've seen before include "Take off" , "Primate resembling a human" , "Send up" , "Closely follow" , "Simulate" .)