Single cat hunted a cuckoo (10)
I believe the answer is:
unattached
'single' is the definition.
(not attached to a partner)
'cat hunted a cuckoo' is the wordplay.
'cuckoo' is an anagram indicator.
'cat'+'hunted'+'a'='cathunteda'
'cathunteda' is an anagram of 'UNATTACHED'.
(Other definitions for unattached that I've seen before include "Not belonging" , "Single" , "independent" , "Not married" , "Not joined" .)