Bully Bishop defeated after argument (8)
I believe the answer is:
browbeat
'bully' is the definition.
(I know that bully can be written as browbeat)
'bishop defeated after argument' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'defeated' becomes 'beat' (I've seen this in another clue).
'after' means one lot of letters go next to another.
'argument' becomes 'row' (to row is to argue).
'beat' after 'row' is 'rowbeat'.
'b'+'rowbeat'='BROWBEAT'
(Other definitions for browbeat that I've seen before include "Bully verbally" , "Intimidate, bulldoze" , "Hector" , "cow" , "Threaten - bully" .)