Pines irrationally for a bird (5)
I believe the answer is:
snipe
'a bird' is the definition.
(snipe is a kind of bird)
'pines irrationally' is the wordplay.
'irrationally' indicates an anagram.
'pines' is an anagram of 'SNIPE'.
'for' is the link.
(Other definitions for snipe that I've seen before include "To pick off soldiers, say" , "Fire from cover; bird" , "Wading bird with long straight bill" , "Verbal criticism" , "Shoot from place of concealment" .)