A flier to greet anew (5)
I believe the answer is:
egret
'a flier' is the definition.
(egret is a kind of birdanimal)
'greet anew' is the wordplay.
'anew' indicates an anagram.
'greet' is an anagram of 'EGRET'.
'to' is the link.
(Other definitions for egret that I've seen before include "Wader with white plumage" , "Type of forty eight Ac" , "young bird" , "Greet (anag) -- wading bird" , "White wading bird" .)