Thirteenth Doctor

Emerging from her predecessor's destructive and explosive regeneration, the Thirteenth Doctor was the second incarnation in the Doctor's second regeneration cycle. After a full regenerative cycle, and a thirteenth regeneration produced only men, this Doctor was notable for being the first female incarnation of the Doctor. However before she had time to adjust to the change the TARDIS began malfunctioning after a push of a button, due to the damage done by the regeneration itself, and the Doctor found herself flung out of the TARDIS, the last she saw of it being the TARDIS dematerializing, the newly regenerated Doctor falling straight down to Earth.

A day to come
When the Twelfth Doctor broke his toe, Clara Oswald suggested regenerating to heal the injury, but he berated the idea as a waste. (PROSE: The Blood Cell)

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, secretly putting blanks in all the guns, and faking his regeneration to complete the illusion. He made it look like the process had started, but emerged as himself to show her that he had deceived her. (TV: The Lie of the Land)

Post-regeneration
After the Twelfth Doctor was gravely wounded by the Cybermen on the Mondasian colony ship, the regenerative process began. However, tired of "being someone else", the Doctor delayed the change for some weeks, (TV: The Doctor Falls) until an encounter with his first incarnation, Archibald Hamish Lethbridge-Stewart, and the Testimony caused the Doctor to concede that another regeneration would not "kill [him]". After taking a final look at the universe and providing advice to his next incarnation, the Doctor regenerated inside his the TARDIS in an explosive fashion.

Staggering to the console in a daze, the new Doctor examined her face in a reflection, finding it "brilliant" to discover she was a female. After pressing a button on the TARDIS' console, the TARDIS suddenly spiralled into chaos, caused in part by the Doctor's explosive regeneration, and the Doctor was thrown out through the TARDIS' doors in the confusion, with the TARDIS itself vanishing without the now falling Doctor. (TV: Twice Upon a Time)

Appearance
This incarnation of the Doctor 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. (TV: World War Three)

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 thirteenth incarnation appeared in The Curse of Fatal Death. The Eighth Doctor was offered the chance to become a woman in the minisode The Night of the Doctor.
 * This is the only known incarnation of the Doctor that is not known to have participated in the Last Great Time War.
 * This is also the only incarnation that is completely unknown to River Song, the only incarnation from the Doctor's new regeneration cycle she last met being the Thirteenth Doctor's predecessor.

ru:Тринадцатый Доктор Decimotercera Doctora