Repeat backing of Church House (4)
I believe the answer is:
echo
'repeat' is the definition.
('echo' can be a synonym of 'repeat')
'backing of church house' is the wordplay.
'backing of' is a reversal indicator.
'church' becomes 'ce' (abbreviation for Church of England).
'house' becomes 'ho' (abbreviation for house).
'ce' backwards is 'ec'.
'ec'+'ho'='ECHO'
(Other definitions for echo that I've seen before include "Response" , "Repetition by reflection" , "Sound following" , "What evokes memories" , "E; reverberation" .)