Gravedigger has lewd message being broadcast (6)
I believe the answer is:
'gravedigger' is the definition.
'lewd message being broadcast' is the wordplay.
'lewd message' becomes 'sext' (I have seen 'Explicit message' mean 'sext' so perhaps 'message' could also mean 'sext'. I am not sure about the 'lewd' bit.**).
'being broadcast' becomes 'on' (I've seen this in other clues).
'has' acts as a link.
Can you help me to learn more?
(Other definitions for sexton that I've seen before include "They went and told the -, and / The - tolled the bell (Thomas Hood)" , "Graveyard employee" , "One looks after church and churchyard" , "parish factotum" , "Church official" .)