Church has included hunt (5)
I believe the answer is:
chase
'hunt' is the definition.
(I know that chase is a is a more specific form of the action of hunt)
'church has included' is the wordplay.
'church' becomes 'CE' (Church of England).
'included' indicates putting letters inside.
'ce' placed around 'has' is 'CHASE'.
(Other definitions for chase that I've seen before include "Engrave - hunt - pursue" , "Pursue; decorate (metal) by engraving" , "Pursuit" , "Hound" , "groove" .)