Schism underpinning quiet confession (6)
I believe the answer is:
shrift
'confession' is the definition.
(shrift is a kind of confession)
'schism underpinning quiet' is the wordplay.
'schism' becomes 'rift' (I've seen this before).
'underpinning' means one lot of letters go next to another (I've seen this in other clues).
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'rift' put after 'sh' is 'SHRIFT'.
(Other definitions for shrift that I've seen before include "Pardon?" , "confession, this might be short" , "Absolution and penance (now usually short!)" , "form of confession" , "Given a short one, one is dismissed" .)