Dismissal, sweeper having received red card? (5-3)
I believe the answer is:
brush-off
'dismissal' is the definition.
(thesaurus)
'sweeper having received red card?' is the wordplay.
'sweeper' becomes 'brush' (something which sweeps).
'having received red card?' becomes 'off' (sent off from a football match).
'brush'+'off'='BRUSH-OFF'
(Other definitions for brush-off that I've seen before include "Rejection, dismissal" , "Curt rejection" .)