3 devouring rook and chicken part (6)
I believe the answer is:
breast
'chicken part' is the definition.
('breast' is part of 'chicken')
'3 devouring rook' is the wordplay.
I cannot really understand how this works, but
'rook' could be 'r' (chess abbreviation) and 'r' is present in the answer.
The remaining letters 'beast' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'and' acts as a link.
Can you help me to learn more?
(Other definitions for breast that I've seen before include "Upper front part of the human torso" , "Chicken portion" , "Manfully oppose" , "Milk supplier" , "Set bar (anag.)" .)