Bishop is hiding a prejudice (4)
I believe the answer is:
bias
'prejudice' is the definition.
('bias' can be a synonym of 'prejudice')
'bishop is hiding a' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'hiding' means one lot of letters goes inside another.
'is' enclosing 'a' is 'ias'.
'b'+'ias'='BIAS'
(Other definitions for bias that I've seen before include "Bigotry" , "(Bowls) irregular shape" , "Spin" , "Large city in Florida" , "Favouritism" .)