Intellectual heard greeting bishop on street (8)
I believe the answer is:
highbrow
'intellectual' is the definition.
(I know that highbrow is a type of intellectual)
'heard greeting bishop on street' is the wordplay.
'heard' shows a homophone (sound like).
'greeting' becomes 'hi' (hi is a kind of greeting).
'bishop' becomes 'B' (chess abbreviation).
'on' says to put letters next to each other.
'street' becomes 'row' (eg Savile Row).
'hi' sounds like 'high'.
'high'+'b'+'row'='HIGHBROW'
(Other definitions for highbrow that I've seen before include "Person of erudite tastes" , "Highly cultured or educated" , "Intellectual - cultured" , "Intellectual with lofty forehead?" .)