No rice is cooked for Caruso for instance (6)
I believe the answer is:
enrico
'for caruso for instance' is the definition.
(opera singer Enrico Caruso, 1873-1921)
'no rice is cooked' is the wordplay.
'is cooked' indicates an anagram (letters cooked into a new form).
'no'+'rice'='norice'
'norice' with letters rearranged gives 'ENRICO'.
(Other definitions for enrico that I've seen before include "Italian Henry like Caruso" , ". . . . . . Caruso (tenor)" .)