Dismissed by the party and overcome (5)
I believe the answer is:
outdo
'overcome' is the definition.
(outdoing is a kind of overcoming)
'dismissed by the party' is the wordplay.
'dismissed' becomes 'out' (dismissed in cricket).
'by' means one lot of letters go next to another.
'the party' becomes 'do' (do can informally mean a party).
'out'+'do'='OUTDO'
'and' is the link.
(Other definitions for outdo that I've seen before include "Best" , "Perform better than, be superior to" , "Overcome" , "Get the better of" , "Exceed" .)