Casually dismiss bishop and hurry away (5,3)
I believe the answer is:
brush off
'casually dismiss' is the definition.
(I've seen this before)
'bishop and hurry away' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'and' means one lot of letters go next to another.
'hurry' becomes 'rush' (synonyms).
'away' becomes 'off' (synonyms).
'b'+'rush'+'off'='BRUSH-OFF'
(Other definitions for brush off that I've seen before include "Refusal to acknowledge" , "Rudely dismiss" , "Curt rejection" , "Casually dismiss" , "Cold shoulder" .)