The Minister

The Minister was a renegade Time Lord, and an associate of the Doctor going as far back as their third incarnation, when the Doctor helped cure the Minister's tenth incarnation of a condition which caused all their incarnations to have the same face, despite alterations in personality. At the time, the Minister had been living on the human colony planet Samael for nine consecutive incarnations, under the alias of Felicity Morgan.

As the Minister of Chance, the Minister was active in two possible versions of reality where a bare few Time Lords were left in the universe.

The Minister's incarnation
In her original life on Gallifrey, the original incarnation of the Minister was genetically modified by the Celestial Intervention Agency genetically modified her so she would be able to retain her appearance across incarnations. Fleeing from Gallifrey in a TARDIS, she entered politics on the planet Samael, where the political system was defined by assassination. Under the name "Felicity Morgan", she was promoted nine times, being assassinated with each promotion and regenerating into the same face, her personality adjusting each time to fit her new position. Only her two closest assistants knew her secret.

In order, she became:
 * the Minister of Fisheries;
 * the Minister of Agriculture;
 * the Minister of Housing;
 * the Minister of Environment;
 * the Minister of Health;
 * the Minister of Education;
 * the Minister of War;
 * the Minister of Industry;
 * the Minister of Foreign Affairs and Diplomacy.
 * The latter's regeneration into the Prime Minister was witnessed by the Third Doctor and Jo Grant, who also helped her realise that she was being manipulated by the Master. With her conset, the Doctor removed the psychic block in her mind which kept all her regenerations the same. Despite planning to leave Samael and actual politics, and knowing that her next regeneration would no longer have the face of "Felicity Morgan", she decided to keep going by "the Minister"; one of her assistants joked that she might adopt the name of "Minister of Luck". (AUDIO: The Same Face)
 * Going by "the Minister of Chance", a "man with a bent nose" travelled as a renegade Time Lord in his TARDIS. In the post-War universe, he became one of the four surviving elementals. (PROSE: The Gallifrey Chronicles, COMIC: Miranda) Another possible path for him, however, was becoming one of the Fraction in a state of reality where Gallifrey was deserted in the Seventh Doctor's lifetime. (WC: Death Comes to Time)
 * Following his "defrocking" by the Seventh Doctor, (WC: Death Comes to Time) the Minister regenerated into a new incarnation who travelled in the universe using the formula for doors instead. (PROSE: The Minister of Chance, etc.)