First Minister of Chance

In an incarnation described in multiple accounts as a "man with a bent nose", the Minister of Chance tried to go good in a universe where he was one of the last few Time Lords.

A day to come
After the Third Doctor and Jo Grant freed the newly-regenerated tenth incarnation of a renegade Time Lord known as the Minister from the manipulations of the Master, the Doctor removed the alteration to her biology that had kept her regenerating into the same face nine times over. Thus, she knew her next regeneration would bring completely new possibilities. However, she reaffirmed her wish to do good, and stated that she would retain the name of "the Minister" even if she was no longer officially a minister of Samael. One of her assistants joked that she might starting calling herself a "Minister of Luck". (AUDIO: The Same Face)

When he looked into a Tomorrow Window and saw his many potential futures, the Eighth Doctor saw not only multiple possible future regenerations of himself, but also a "man with a bent nose", wearing a cream suit and strolling through Regent's Park. His long hair was swept back and his chin was held "imperiously high". (PROSE: The Tomorrow Windows) He would later see the "man with a bent nose" again as part of a vision of the four Time Lords who survived the War in Heaven, alongside the man with the rosette, a blonde woman, and his own future self the Emperor. In the vision, the man appeared tall, wore a cravat, and held a pair of dice. (PROSE: The Gallifrey Chronicles)

Thwarting Tannis
In a reality where the Seventh Doctor became the last of the Time Lords and seemingly sacrificed himself fighting Tannis, (WC: Death Comes to Time) which one account suggested was a parallel universe distinct from the world of the Eighth Doctor who encountered the Divergent Universe, (AUDIO: Zagreus) although another account acknowledged the Canisian invasion as an event in the Eighth Doctor's past, (PROSE: Trading Futures) the Minister thwarted General Tannis' plans to infect the planet Alnelan with a deadly plague, but his female assistant "wandered off" on the planet.

Following his defeat Tannis agreed to the Treaty of Karselai and signed away any rights to alien planets. Despite this, the Canisian military, led by Tannis, brutally conquered the Santine Republic, confining the leading members of the Republic to a prison camp. The Minister, who was able to transfer a virus to a Canisian computer via speech, seeded a rebellion on Santiny while the Seventh Doctor investigated the deaths of two Time Lords on Earth. Tannis was also working towards wiping out the last members of the Fraction, and by massacring the Santine prisoners he provoked the Minister into breaking the rules about non-interference and destroy the fleet.

Due to the Minister's violation of the rules, the Doctor was forced to confront him and revoke his TARDIS. (WC: Death Comes to Time)

Later fate
In a direct consequence of his TARDIS being "revoked" by the Doctor, (WC: Death Comes to Time) the Minister instead learned to travel between worlds using the formula for doors. In a new incarnation who retained the name of "Minister of Chance", he met Kitty in Tantillion and travelled with her as he fought Rathen. (PROSE: The Minister of Chance)

As one of the four surviving elements
In an account which highlighted that Tannis had yet to be defeated, setting it as a different version of history (PROSE: The Gallifrey Chronicles) from the events surrounding the Canisian invasion, (WC: Death Comes to Time) one of the four surviving elementals who survived the War in Heaven was a "man with a bent nose" (PROSE: The Gallifrey Chronicles) who had cut his hair short. (COMIC: Miranda)

Behind the scenes
As spelled out by Lance Parkin in his reference book AHistory, the "man with a bent nose" mentioned in two of the BBC Eighth Doctor Adventures is indeed the Minister of Chance.