Shanty carried by church channel (5)
I believe the answer is:
chute
'channel' is the definition.
(chute is a kind of channel)
'shanty carried by church' is the wordplay.
'shanty' becomes 'hut' (synonyms).
'carried by' means one lot of letters goes inside another.
'church' becomes 'CE' (abbreviation for Church of England).
'hut' inserted into 'ce' is 'CHUTE'.
(Other definitions for chute that I've seen before include "Waterfall" , "Sloping trough" , "Flume" , "Sloping channel" , "Inclined channel for rubbish, laundry etc" .)