Leaderless chaps supporting Anglicanism apply (7)
I believe the answer is:
enforce
'apply' is the definition.
('enforce' can be a synonym of 'apply')
'leaderless chaps supporting anglicanism' is the wordplay.
'leaderless' means to remove the first letter.
'chaps' becomes 'men' (I've seen this before).
'supporting' becomes 'for'.
'anglicanism' becomes 'ce' (abbreviation for Church of England).
'men' with its initial letter taken away is 'en'.
'en'+'for'+'ce'='ENFORCE'
(Other definitions for enforce that I've seen before include "exercise" , "Strictly implement" , "Put into effect" , "Administer with pressure (70" , "Compel or impose obedience, say to law" .)