Nice graph represented vicar's work (9)
I believe the answer is:
preaching
'vicar's work' is the definition.
'nice graph represented' is the wordplay.
'represented' indicates anagramming the letters.
'nice'+'graph'='nicegraph'
'nicegraph' with letters rearranged gives 'PREACHING'.
(Other definitions for preaching that I've seen before include "Delivering a sermon" , "Delivering speech" , "minister's job" .)