A delivery flier (5)
I believe the answer is:
stork
I believe this clue is a double definition.
'a delivery' is the first definition.
(thesaurus)
'flier' is the second definition.
(stork is a kind of birdanimal)
(Other definitions for stork that I've seen before include "Large wading bird" , "The baby bird, so to speak" , "Long-legged bird" , "Baby-carrying bird?" , "Bird that delivers babies?" .)