Old ascetic conceals cold heart (7)
I believe the answer is:
essence
'heart' is the definition.
(I have seen 'The heart' mean 'essence' so perhaps 'heart' could also mean 'essence')
'old ascetic conceals cold' is the wordplay.
'old ascetic' becomes 'essene' (member of historic Jewish sect).
'conceals' indicates putting letters inside.
'cold' becomes 'c' (eg on taps).
'essene' going around 'c' is 'ESSENCE'.
(Other definitions for essence that I've seen before include "Extract; intrinsic nature" , "Intrinsic quality" , "Perfume; core" , "Concentration; nub" , "Intrinsic nature (of something)" .)