Bishop, not well, gives account (4)
I believe the answer is:
bill
'account' is the definition.
(I know that account can be written as bill)
'bishop not well' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'not well' becomes 'ill' ('ill' is the opposite to 'well').
'b'+'ill'='BILL'
'gives' acts as a link.
(Other definitions for bill that I've seen before include "informing of damage" , "Cosby or Clinton?" , "List of charges" , "following 28 [SILVER]" , "The fellow" .)