Strengthen control in favour of church (9)
I believe the answer is:
reinforce
'strengthen' is the definition.
(I know that reinforce is a more specific form of the action strengthen)
'control in favour of church' is the wordplay.
'control' becomes 'rein' (synonyms).
'in favour of' becomes 'for' (being for a particular cause).
'church' becomes 'CE' (abbreviation for Church of England).
'rein'+'for'+'ce'='REINFORCE'
(Other definitions for reinforce that I've seen before include "Buttress" , "Strengthen or support with confrerie" , "Make stronger" , "give added support" , "increase support" .)