Black stuff with core of soft or hard material (5)
I believe the answer is:
copal
'hard material' is the definition.
'black stuff with core of soft' is the wordplay.
'black stuff' becomes 'coal'.
'with core of' is an insertion indicator.
'soft' becomes 'p' (musical abbreviation for 'piano').
'coal' going around 'p' is 'COPAL'.
'or' is the link.
(Other definitions for copal that I've seen before include "Aromatic tree resin" , "Hard resin" , "Resin used in varnish" .)