Eagle, possibly, or parrot, possibly (6)
I believe the answer is:
raptor
'eagle possibly' is the definition.
(eagle is a kind of raptor)
'parrot possibly' is the wordplay.
'possibly' is an anagram indicator.
'parrot' is an anagram of 'RAPTOR'.
'or' is the link.
(Other definitions for raptor that I've seen before include "Harrier possibly" , "Parrot (anag) - bird of prey" , "Eagle, hawk, falcon or owl - parrot (anag)" , "Hunter" .)