Flier making delivery? (5)

I believe the answer is:

stork

I believe this clue is a double definition.

'flier' is the first definition.
(stork is a kind of birdanimal)

'delivery?' is the second definition.
(thesaurus)

'making' is the link.

(Other definitions for stork that I've seen before include "Long-legged bird" , "Baby-carrying bird?" , "The baby bird, so to speak" , "Mythological baby-bringer" , "Large wading bird" .)

I've seen this clue in the Evening Standard.

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