Greet cuckoo and another bird (5)
I believe the answer is:
egret
'bird' is the definition.
(egret is a kind of bird)
'greet cuckoo' is the wordplay.
'cuckoo' is an anagram indicator.
'greet' with letters rearranged gives 'EGRET'.
'and another' acts as a link.
(Other definitions for egret that I've seen before include "White-plumed wader" , "Greet (anag) -- wading bird" , "White, plumed waterbird" , "White wading bird" , "Wading bird like a heron" .)