Purge has a tendency to divide religious establishment (7)
I believe the answer is:
cleanse
'purge' is the definition.
(I've seen this before)
'has a tendency to divide religious establishment' is the wordplay.
'has a tendency' becomes 'leans' ('lean' can be a synonym of 'have a tendency').
'to divide' is an insertion indicator (inserted letters divide the word).
'religious establishment' becomes 'CE' (Church of England).
'leans' going within 'ce' is 'CLEANSE'.
(Other definitions for cleanse that I've seen before include "Make free from dirt" , "Wash" , "subject to purification" , "Free of sin" , "give absolution" .)