Fine evangelist has accidental success (5)
I believe the answer is:
fluke
'accidental success' is the definition.
(I've seen this before)
'fine evangelist' is the wordplay.
'fine' becomes 'f' (abbreviation).
'evangelist' becomes 'Luke' (one of the four Christian evangelists).
'f'+'luke'='FLUKE'
'has' acts as a link.
(Other definitions for fluke that I've seen before include "flounder" , "One lucky" , "Lucky break" , "Accidental success" , "land, by chance" .)