Intellectual argument started by eminent bishop (8)
I believe the answer is:
highbrow
'intellectual' is the definition.
('highbrow' can be similar in meaning to 'intellectual')
'argument started by eminent bishop' is the wordplay.
'argument' becomes 'row' (I've seen this before).
'started by' is a charade indicator (letters next to each other).
'eminent' becomes 'high' ('high' can be a synonym of 'eminent').
'bishop' becomes 'b' (abbreviation used in chess).
'high'+'b'='highb'
'row' put after 'highb' is 'HIGHBROW'.
(Other definitions for highbrow that I've seen before include "Highly cultured or educated" , "Intellectual with lofty forehead?" , "Intellectual - cultured" , "Person of erudite tastes" .)