The flier possibly hurts his head! (6)
I believe the answer is:
thrush
'the flier' is the definition.
(thrush is a kind of birdanimal)
'possibly hurts his head' is the wordplay.
'possibly' is an anagram indicator.
'head' suggests taking the first letters.
The first letter of 'his' is 'h'.
'hurts' anagrammed gives 'thrus'.
'thrus'+'h'='THRUSH'
(Other definitions for thrush that I've seen before include "Flyer" , "Songbird with brownish back and speckled breast" , "Speckle-breasted songbird" , "Small bird - fungal mouth infection" , "Bird that sings" .)