Unconventional priest elected on extreme gamble (6)
I believe the answer is:
fringe
'unconventional' is the definition.
(fringe can mean unconventional or specialist)
'priest elected on extreme gamble' is the wordplay.
'priest' becomes 'fr' (abbreviation for father).
'elected' becomes 'in' (in government).
'on' is a charade indicator (letters next to each other).
'extreme' suggests removing the centre.
'gamble' with its middle removed is 'ge'.
'fr'+'in'+'ge'='FRINGE'
(Other definitions for fringe that I've seen before include "Outer edge; hair over forehead" , "Less important" , "bang of Detroit" , "(Decorative) border" , "Rim" .)