Church worker is to keep sending rude messages (6)
I believe the answer is:
sexton
'church worker' is the definition.
(I've seen this before)
'to keep sending rude messages' is the wordplay.
I cannot quite understand how this works, but
'to' is within the answer.
This explanation may well be incorrect...
'is' is the link.
(Other definitions for sexton that I've seen before include "Graveyard employee" , "Person who looks after church and churchyard" , "Sacristan" , "Job" , "Church functionary" .)