Incident after old bishop's rude (7)
I believe the answer is:
obscene
'rude' is the definition.
(obscene can mean rude or indecent)
'incident after old bishop's' is the wordplay.
'incident' becomes 'scene' (scene is a kind of incident).
'after' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'bishop' becomes 'B' (chess abbreviation).
'o'+'b'='ob'
'scene' put after 'ob' is 'OBSCENE'.
(Other definitions for obscene that I've seen before include "Bawdy" , "Shocking" , "coarse!" , "Offensive - indecent" , "Salacious" .)