A Supreme Dalek was a Black Dalek and the leader of the Renegade Daleks that opposed the Imperial Daleks commanded by Davros, now calling himself the Dalek Emperor. It formed an alliance with The Association led by George Ratcliffe to obtain the Hand of Omega. The Dalek Supreme ended up as the last surviving member of the Renegade Daleks during the Shoreditch Incident after a skirmish with the Imperial Daleks, where the Hand of Omega was taken by the triumphant Imperials. The Seventh Doctor convinced it that it had no purpose. At this point, in a state of confusion and distress, it destroyed itself, breaking the link with Judith Winters. (TV: Remembrance of the Daleks)
It's connection with Judith Winters caused the Supreme Dalek problems; the girl's human emotions would filter into the Daleks' mind when she was accessing the battle computer, treating each problem as nothing more than a game, and causing strange thoughts for the Dalek.
Physically, the connection also made the Dalek's sluggish heartbeat race beyond the safety parameters, forcing the life-support computer in its casing to increase the amount of tranquilisers pumped into its body, making it difficult for the Dalek to concentrate properly. (PROSE: Remembrance of the Daleks)
This Supreme Dalek was mainly black, but had silver sensor globes, shoulder slats, gunstick and neck rings, orange dome-lights, and a less-tapered "skirt" section.