Strengthen control on behalf of Church of England (9)
I believe the answer is:
reinforce
'strengthen' is the definition.
(reinforcing is a kind of strengthening)
'control on behalf of church of england' is the wordplay.
'control' becomes 'rein' (rein is a kind of control).
'on behalf of' becomes 'for' (I've seen this before).
'church of england' becomes 'ce' (abbreviation).
'rein'+'for'+'ce'='REINFORCE'
(Other definitions for reinforce that I've seen before include "Make stronger" , "give added support" , "provide support" , "Buttress" , "increase support" .)