Draw a secretive cuckoo (10)
I believe the answer is:
eviscerate
'draw' is the definition.
(synonyms)
'a secretive cuckoo' is the wordplay.
'cuckoo' indicates an anagram.
'a'+'secretive'='asecretive'
'asecretive' with letters rearranged gives 'EVISCERATE'.
(Other definitions for eviscerate that I've seen before include "Remove essential parts" , "Disembowel" , "Draw" .)