The stony residue from burned coal or from a furnace.

See also: clinker (music)

The Mistake Not…, a Culture vessel of indefinite age, hazy provenance and indeterminate class but generally reckoned to be some sort of modestly tooled-up civilian craft rather than a part of the Culture’s allegedly still slowly shrinking military resources, had been detailed to rendezvous with the Liseiden fleet by the clinker sun of Ry. … it circled the husk that was the long-dead sun for a while, inspecting the tiny, barely radiating stellar remnant … [which] lay burned out now, as cold as its accompanying planets and darker than the galactic skies around it.

Definition from Kindle (The New Oxford American Dictionary)