Want chess player to lose bishop (4)
I believe the answer is:
lack
'want' is the definition.
('lack' can be a synonym of 'want')
'chess player to lose bishop' is the wordplay.
'chess player' becomes 'black' (I've seen this before).
'to lose' indicates named letters should be taken away.
'bishop' becomes 'b' (abbreviation used in chess).
'black' with 'b' removed is 'LACK'.
(Other definitions for lack that I've seen before include "Shortage" , "Deficiency or want" , "Be without, need" , "Deficiency (of something)" , "Be wanting or without" .)