Fugitive Doctor

An incarnation of the Doctor, identified as such by the Judoon and the Thirteenth Doctor's sonic screwdriver, had a history of working for Gallifrey, in a role one did not "apply for", which she sought, though failed, to abandon. At one point, the Doctor hid out on Earth using a Chameleon Arch, taking on a human identity as "Ruth Clayton".

She had her TARDIS buried near the lighthouse where she stored her true identity, and trusted Lee Clayton to protect her, under cover as Ruth's husband. Lee was also tasked with reminding her to "Follow the light and break the glass" when the time was right, as this would lead Ruth to return to the lighthouse, which she was made to recall from childhood, and finally restore her Time Lord memories. (TV: Fugitive of the Judoon)

Working for the Time Lords
At one point, she worked for the Time Lords. She tried to flee from this job that she hadn't signed up for by disguising herself as a human. (TV: Fugitive of the Judoon)

As Ruth Clayton
When questioned by the Thirteenth Doctor, Ruth explained that she was brought up by her parents, who lived in a disused lighthouse. Although she adored them, she moved away from the quiet location, rationalising it as an act of rebellion against her parents. She moved to Gloucester in mid-December 1999. Although her parents were buried at the lighthouse, which they bequeathed to Ruth, she never returned to her former home before travelling there with the Doctor.

Ruth lived in Gloucester with her "husband", Lee. She worked there as a self-employed tour guide, and was a regular customer at a coffee shop where she knew the barista, Allan. Allan tried to convince Ruth that Lee was not good enough for her, even keeping a dossier which recorded his suspicions of him.

The Judoon were able to track the couple due to Lee's sentimentality in keeping an old service medal. Lee distracted the Judoon, allowing Ruth to escape with the Doctor, but sent her a cryptic message, and was ultimately killed by Gat. Ruth and the Doctor then travelled to the lighthouse where she broke the biodata module and reactivated her Time Lord personality. (TV: Fugitive of the Judoon)

Memories restored
With her true self restored, she retrieved a rifle belonging to Gat, changed her clothes, and went outside to introduce herself to the Thirteenth Doctor, who had dug up the TARDIS. She then teleported the two of them onboard, where she learned who the Thirteenth Doctor was. Since she didn't recognise her, she assumed she was encountering a future incarnation of herself, only to learn that the Thirteenth Doctor had no memory of ever being her.

Before either Doctor could figure out what was going on, the TARDIS was captured by the Judoon. Onboard the Judoon ship, the two Doctors encountered Gat, with the Doctor giving Gat back her rifle. She attempted to pass off her other self as nobody, but this didn't work, with the Thirteenth Doctor revealing her identity. To her surprise, the Thirteenth Doctor claimed that Gallifrey had been destroyed and showed her memory of it to Gat. Gat then tried to execute the two Doctors, despite the Doctor begging her not to go through with it, only for the rifle, which the Doctor had sabotaged, to backfire on her, killing her. Ignoring the Thirteenth Doctor's horror at this, the Doctor picked up the rifle and corrected the sabotage. She threatened the Judoon, pointing out that since their ship is now in interstellar space, they have no jurisdiction and thus no crime was committed, forcing the Judoon to let the two Doctors go. The Doctor returned the Thirteenth Doctor to Earth, noting that both of them can't be right about their past. (TV: Fugitive of the Judoon)

Personality
The Doctor exhibited a more violent persona than her other incarnations, threatening to kill a Judoon platoon, and arming herself with a gun, even though she acknowledged that "the Doctor never uses weapons".

She also showed dislike for the Thirteenth Doctor, dismissing her initially as her future. She was later furious with the Thirteenth Doctor for interfering in her plans for Gat. (TV: Fugitive of the Judoon)

Habits and quirks
To be added

Skills
The Doctor had the combat skills to overpower a platoon of Judoon with her bare hands, and even had the strength to remove Captain Pol-Kon-Don's horn. (TV: Fugitive of the Judoon)

Appearance
To be added

Main attires
The Doctor wore a long, navy blue coat. (TV: Fugitive of the Judoon)

Behind the scenes
While Fugitive of the Judoon left it unclear where this incarnation of the Doctor fits into the Doctor's life, Chris Chibnall confirmed to Mirror that; "She is definitively the Doctor. There's not a sort of parallel universe going on, there's no tricks."

Casting
This incarnation of the Doctor was the first within the DWU to be played by a non-white actor, Jo Martin. Some stories have previously shown the Doctor briefly taking over the bodies of non-white humans, and so getting played by those who were cast for those characters, and others have already indicated that non-white incarnations do in fact exist somewhere along the Doctor's timeline.

In 1986, Lenny Henry also portrayed a parodic incarnation of the Doctor in a comedy sketch as part of his BBC series The Lenny Henry Show.

Daniel Anthony played the Eleventh Doctor in The Sarah Jane Adventures story Death of the Doctor while he occupied the body of Clyde Langer, and Damian Lynch played the Third Doctor in the audio story Ghost in the Machine while he was using the body of Benjamin Chikoto to communicate.

More concretely, Russell T Davies' Rose novelisation shows that Clive Finch has collected a photograph of, among other known incarnations, a tall, bald, black female Doctor who wields a flaming sword.