Heart perhaps that's stopped in church? (5)
I believe the answer is:
I believe this clue is a double definition.
'heart perhaps' is the first definition.
(the heart is an example)
'that's stopped in church' is the second definition.
(a church organ contains stops)
(Other definitions for organ that I've seen before include "Medium; body part" , "Wurlitzer, for example" , "Mouthpiece" , "Soft part of the body which has a specific function" , "Air-powered instrument" .)