Rejection making bishop hurry away (5,3)
I believe the answer is:
brush off
'rejection' is the definition.
(I know that brush-off is a type of rejection)
'bishop hurry away' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'hurry' becomes 'rush' (synonyms).
'away' becomes 'off' (synonyms).
'b'+'rush'+'off'='BRUSH-OFF'
'making' acts as a link.
(Other definitions for brush off that I've seen before include "Rudely dismiss" , "Refusal to acknowledge" , "Cold shoulder" , "Snub" , "Curt rejection" .)