Unorthodox denomination of revolutionary church in street (4)
I believe the answer is:
sect
'unorthodox denomination' is the definition.
(an unorthodox denomination of a faith)
'revolutionary church in street' is the wordplay.
'revolutionary' is a reversal indicator.
'church' becomes 'CE' (abbreviation for Church of England).
'in' is an insertion indicator.
'street' becomes 'st' (abbreviation).
'ce' written backwards gives 'ec'.
'ec' going within 'st' is 'SECT'.
'of' acts as a link.
(Other definitions for sect that I've seen before include "Denomination" , "Breakaway group" , "Fringe religious group" , "Religious faction" , "Dissenting body" .)