Old boy finds part of a play disgusting (7)
I believe the answer is:
obscene
'disgusting' is the definition.
(obscene can mean disgusting or indecent)
'old boy finds part of a play' is the wordplay.
'old boy' becomes 'OB' (abbreviation for a private school 'old boy').
'finds' is a charade indicator (letters next to each other).
'part of a play' becomes 'scene' ('scene' is part of 'play').
'ob'+'scene'='OBSCENE'
(Other definitions for obscene that I've seen before include "Improper" , "X-rated" , "One's CBE (anag)" , "Offensive - indecent" , "off colour?" .)