Flier almost out of breath? (6)
I believe the answer is:
puffin
'flier' is the definition.
(puffin is a kind of birdanimal)
'almost out of breath?' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'out of breath?' becomes 'puffing' (puffing can mean out of breath or panting).
'puffing' with its final letter taken away is 'PUFFIN'.
(Other definitions for puffin that I've seen before include "Bright-billed auk" , "Bright-billed bird" , "Northern seabird with short neck and brightly coloured bill" , "Seabird with parrot-like beak" , "Bird with large beak" .)