Persist in performing vile rap (7)
I believe the answer is:
prevail
'persist in' is the definition.
(prevailing is a kind of persisting in)
'performing vile rap' is the wordplay.
'performing' indicates an anagram.
'vile'+'rap'='vilerap'
'vilerap' is an anagram of 'PREVAIL'.
(Other definitions for prevail that I've seen before include "Successfully persuade" , "Carry the day" , "Exist generally" , "Win through" , "Get one's way" .)