Religious person shaves his own jet, bizarrely (8,7)
I believe the answer is:
jehovahs witness
'religious person' is the definition.
(Jehovah's Witness is an example)
'shaves his own jet bizarrely' is the wordplay.
'bizarrely' indicates an anagram.
'shaves'+'his'+'own'+'jet'='shaveshisownjet'
'shaveshisownjet' with letters rearranged gives 'JEHOVAHS WITNESS'.
(Other definitions for jehovahs witness that I've seen before include "sectarian" , "one preaching the Second Coming" .)