Black Dalek Leader

The Black Dalek, also holding the rank of Supreme Dalek, was the second-in-command of the Dalek race, (PROSE: The Evil of the Daleks) after the Dalek Prime. (PROSE: The Chase, The Mutation of Time)

Biography
After the failure of the 22nd century Dalek invasion of Earth, the Daleks identified the Doctor and the Black Dalek, under orders from the Dalek Prime, (PROSE: The Chase) ordered an assassination squad to pursue his TARDIS in a Dalek time machine. The squad failed. (TV: The Chase) Some human historians believed, on the other hand, that the Supreme Dalek had only launched on that particular mission much later in its (and the Daleks') history, spurred to action by the destruction of its fellow Dalek Councilmember the Gold Dalek. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)

At any rate, the same Black Dalek, acting as a Supreme Dalek, oversaw the Dalek operations on planet Kembel in the year 4000. It led the conference which founded the Great Alliance with the emissaries from the Outer Galaxies, intent on invading the solar system. (TV: Mission to the Unknown, PROSE: Mission to the Unknown, WC: Mission to the Unknown) It was, by then, the last surviving member of the Dalek Council, hence having adopted the title of singular Dalek Supreme. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)

Some months later, the Supreme Dalek held another conference as the Alliance completed preparations on the Time Destructor with the taranium supplied by Mavic Chen. The theft of the taranium by the First Doctor put the Black Dalek on edge, and it callously executed a number of its erstwhile allies, and even other Daleks, for failure during the recovery efforts.

Even after the successful recovery of the taranium core, the Doctor, Steven Taylor and Sara Kingdom managed to hijack the Time Destructor itself, using the Black Dalek as a shield to discourage the other Daleks from attacking them. The active Time Destructor wiped out all Daleks on the planet. (TV: The Dalek's Master Plan) This was a massive blow for the Dalek Empire as the Dalek Prime considered both the fleet and the Black Dalek irreplaceable. (PROSE: The Mutation of Time) By another account however, the Black Dalek had survived the Time Destructor's detonation, though it was badly damaged and left in critical condition, having been recovered by attendants and brought back to Dalek territory. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)

When the Second Doctor returned to Skaro, he encountered another Black Dalek. He wondered if it was the same one from Kembel, having survived, but there were many other Black Daleks throughout the City. (PROSE: The Evil of the Daleks)

Behind the scenes

 * John Peel's novelisations establish the Black Dalek from The Chase and The Daleks' Master Plan as one and the same. Reference to this Dalek being "irreplaceable" in The Mutation of Time also heavily implies it to be the same individual as the Black Dalek Leader featured prominently throughout The Dalek Chronicles, a link further drawn by the reference to this Dalek being "the second in command of the Daleks race" included in the novelisation of The Evil of the Daleks.
 * In a similar vein, this could also be the Dalek Supreme seen in Daughter of the Gods, which takes place in an alternate timeline in which the Daleks successfully develop the Time Destructor.
 * The Supreme Dalek was voiced by either David Graham or Peter Hawkins in its original televised appearances. Nicholas Briggs provided its voice for the novelisation audiobooks, as well as the reconstruction of Mission to the Unknown by the University of Central Lancashire.