Kitty eating a bishop's bird (6)
I believe the answer is:
parrot
'bird' is the definition.
(parrot is a kind of bird)
'kitty eating a bishop's' is the wordplay.
'kitty' becomes 'pot' ('pot' can be a synonym of 'kitty'**).
'eating' means one lot of letters goes inside another.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'a'+'rr'='arr'
'pot' placed around 'arr' is 'PARROT'.
(Other definitions for parrot that I've seen before include "Recite" , "Repeat unintelligently" , "18's [BIRD]" , "Tropical bird for Pat Orr" , "Eg, macaw" .)