Thirteenth Doctor

After an explosive and destructive regeneration, the Thirteenth Doctor emerges. After a full regenerative cycle, and a thirteenth regeneration, produced only men, this Doctor was the second regeneration of the Doctor's second regeneration cycle, and the first female incarnation of any regeneration cycle. However, when this Doctor sees her new face, the TARDIS throws her out, leaving her falling to Earth as it dematerialised.

A day to come
While suffering from the common cold, the Twelfth Doctor, overreacting to the illness, considered the possibility of regenerating. (COMIC: The Day at the Doctors)

After the Monk invasion, the Twelfth Doctor needed to know if his companion, Bill Potts, was under the control of the Monks, and deceived her into shooting him in a rage to see if she had succumbed to the mind control, faking his regeneration to complete the illusion. He made it look like the process had started, but emerged as himself to show her that she had been deceived by him. (TV: The Lie of the Land)

The Twelfth Doctor had been gravely wounded by the Cybermen on the Mondasian colony ship. In spite of his life-threatening injury, the Doctor, feeling tired of "being someone else", chose to purposefully halt his regenerative process. (TV: The Doctor Falls) However, following an encounter with his first incarnation, who had held similar reservations before his own regeneration, (TV: The Tenth Planet) and the Testimony, the Doctor ultimately conceded that another regeneration would not "kill [him]."

Returning to the TARDIS, the Doctor addressed himself or rather his successor, offering words of advice before finally regenerating. (TV: Twice Upon a Time)

Post-regeneration
Immediately after, the Doctor examined her new face in a reflection. She simply smiled and exclaimed "Oh, brilliant!" However, before she could continue, the TARDIS suddenly fell out of her control, thanks to the explosive prolonged regeneration of her predecessor, and the Doctor found herself falling out through the TARDIS' now opened doors to the Earth below, with the TARDIS itself dematerialising without the Doctor. (TV: Twice Upon a Time)

Appearance
She resembled a woman in her mid-thirties, with medium length blonde hair and hazel-coloured eyes. She had a Northern accent, much like her ninth incarnation.

Her hands were noticeably smaller than those of her predecessor, resulting in the ring that he had worn falling onto the floor upon regeneration, and she was shorter in stature as well. (TV: Twice Upon a Time)

Behind the scenes

 * Female incarnations of the Doctor have previously appeared in Doctor Who Unbound and non-valid material. A female Third Doctor appeared in Exile, and another, also a thirteenth incarnation, appeared in The Curse of Fatal Death.