Garment that's a source of penance in church (4)
I believe the answer is:
cape
'garment' is the definition.
(cape is a kind of garment)
'a source of penance in church' is the wordplay.
'source of' suggests taking the first letters.
'in' means one lot of letters goes inside another.
'church' becomes 'ce' (abbreviation for Church of England).
The first letter of 'penance' is 'p'.
'a'+'p'='ap'
'ap' inserted into 'ce' is 'CAPE'.
'that's' is the link.
(Other definitions for cape that I've seen before include "Head; garment" , "Loose cloak or promontory" , "Wrath perhaps" , "Headland - garment" , "Cloak, robe" .)