Incurred expenditure on behalf of church that's no longer influential (5,5)
I believe the answer is:
spent force
'that's no longer influential' is the definition.
(something that has lost power or influence)
'incurred expenditure on behalf of church' is the wordplay.
'incurred expenditure' becomes 'spent' (spent money).
'on behalf of' becomes 'for' (eg speaking on behalf of or for someone else).
'church' becomes 'CE' (abbreviation for Church of England).
'spent'+'for'+'ce'='SPENT FORCE'
(Other definitions for spent force that I've seen before include "power exhausted" , "Has-been" .)