Cleric rejected papers cutting about sex (8)
I believe the answer is:
cardinal
'cleric' is the definition.
(I've seen this before)
'rejected papers cutting about sex' is the wordplay.
'rejected' says the letters should be written backwards.
'papers' becomes 'ID' (identification papers).
'cutting' means one lot of letters goes inside another (some letters cut their way into a word).
'about sex' becomes 'carnal' (carnal can mean relating to sex).
'id' backwards is 'di'.
'di' put into 'carnal' is 'CARDINAL'.
(Other definitions for cardinal that I've seen before include "Main point of compass - most important" , "Counsellor to the Pope" , "High-ranking official of the Roman Catholic church" , "of prime importance" , "of the highest importance" .)