Waste of mine left in sink (4)
I believe the answer is:
slag
'waste of mine' is the definition.
(waste matter created by mining)
'left in sink' is the wordplay.
'left' becomes 'l' (common abbreviation).
'in' is an insertion indicator.
'sink' becomes 'sag' (sagging is a kind of sinking).
'l' inserted inside 'sag' is 'SLAG'.
(Other definitions for slag that I've seen before include "Smelted-ore refuse" , "Smelting or coal waste" , "dissolute man (more recently)" , "Cinders could become this" , "Solid waste matter as from mine or smelter" .)