Monster devouring rook and chicken part (6)
I believe the answer is:
breast
'chicken part' is the definition.
('breast' is part of 'chicken')
'monster devouring rook' is the wordplay.
'monster' becomes 'beast' (I've seen this before).
'devouring' is an insertion indicator.
'rook' becomes 'r' (abbreviation in chess).
'beast' going around 'r' is 'BREAST'.
'and' is the link.
(Other definitions for breast that I've seen before include "Milk producer" , "Get on top" , "Outstanding feature" , "flesh" , "face" .)