Hard mineral, not fine material (4)
I believe the answer is:
lint
'material' is the definition.
(lint is a kind of material)
'hard mineral not fine' is the wordplay.
'hard mineral' becomes 'flint' (I've seen this before).
'not' indicates named letters should be taken away.
'fine' becomes 'f' (abbreviation).
'flint' with 'f' taken away is 'LINT'.
(Other definitions for lint that I've seen before include "Fabric for dressings" , "Fabric for dressing wounds" , "Soft material for dressing wounds" , "Absorbent material for dressing wounds" , "Soft cloth for dressing wounds" .)