My pet cuckoo is vain (5)
I believe the answer is:
empty
'vain' is the definition.
(I've seen this before)
'my pet cuckoo' is the wordplay.
'cuckoo' indicates an anagram.
'my'+'pet'='mypet'
'mypet' is an anagram of 'EMPTY'.
'is' acts as a link.
(Other definitions for empty that I've seen before include "Evacuate" , "Unfilled" , "Arabic quarter" , "(Of words) insincere" , "Hollow or vacant" .)