Object on bishop’s crook (4)
I believe the answer is:
bend
'crook' is the definition.
('bend' can be a synonym of 'crook')
'object on bishop's' is the wordplay.
'object' becomes 'end' (I've seen this in other clues**).
'on' means one lot of letters go next to another.
'bishop' becomes 'b' (abbreviation used in chess).
'end' after 'b' is 'BEND'.
(Other definitions for bend that I've seen before include "It may be sinister" , "Stoop; (heraldic) stripe" , "Lean forward" , "Crouch" , "Stoop; knot" .)