Quarry with hard core (4)
I believe the answer is:
pith
'core' is the definition.
(I've seen this before)
'quarry with hard' is the wordplay.
'quarry' becomes 'pit' ('pit' can be a synonym of 'quarry').
'with' is a charade indicator (letters next to each other).
'hard' becomes 'h'.
'pit'+'h'='PITH'
(Other definitions for pith that I've seen before include "Lining of rind - important part" , "nub of matter" , "Core - essence" , "Tissue inside the rind of citrus fruits" , "Spongy tissue like that lining an orange skin" .)