Service provider enquires intrusively over time (6)
I believe the answer is:
priest
'service provider' is the definition.
(a priest might provide a church service)
'enquires intrusively over time' is the wordplay.
'enquires intrusively' becomes 'pries' (as in prying into someone else's affairs).
'over' says to put letters next to each other.
'time' becomes 't' (abbreviation).
'pries'+'t'='PRIEST'
(Other definitions for priest that I've seen before include "Member of the clergy" , "with orders" , "Church minister" , "Art spy" , "Conductor of religious service" .)