Clara's TARDIS

Clara's TARDIS was a TARDIS that was piloted by Clara Oswald and Ashildr/"Me" after having left the Twelfth Doctor's company. With a broken chameleon circuit, it adopted the form of a 1950s American diner.

Theft
The Doctor plucked Clara away from her death by the Quantum Shade through the use of an extraction chamber, they retreated into the Cloisters, where they were followed by the Twelfth General, Ohila and Gastron. Clara distracted the Time Lords while the Doctor escaped and stole this TARDIS much like he had stolen his own TARDIS. He then piloted it back in time a few minutes to materialise around Clara and rescue her from the General and Ohila who were trying to find out what the Doctor knew about the Hybrid.

In an attempt to shake off the Time Lords, the Doctor piloted the TARDIS to the end of the universe, where he was reunited with Me. There, the two discussed the Hybrid, and their theories on what it was before the Doctor revealed that he planned to wipe Clara's memory of him so that she could live a normal life again and not be found by the Time Lords. However, having listened in on this conversation, Clara used the sonic sunglasses to "reverse the polarity" of the memory-wiping device and revealed this fact when the Doctor and Me entered the TARDIS. Not knowing which one of them would lose their memory of the other, both Clara and the Doctor held the device. The Doctor ended up wiping his own memory of Clara.

Clara, now on the run from the Time Lords, piloted the TARDIS to Nevada where she dropped the Doctor off in the care of a man. She then recovered the Doctor's TARDIS from London and transported it to Nevada. Clara and Me landed their TARDIS nearby, where it took the form of a diner. The Doctor later came across the diner where Clara was working as a waitress. She gave him a lemonade and he proceeded to tell the story of his adventures on Gallifrey.

After realising there was no way to make the Doctor remember her, Clara bade the Doctor farewell, entering the console room of her TARDIS through a rear door in the diner where Me was waiting. The TARDIS dematerialised, leaving behind the Doctor and his own TARDIS. Me later told Clara that she couldn't get the chameleon circuit working, leaving the TARDIS stuck as a diner.

With Clara noting that her death was a fixed point in time, she resolved to return to Gallifrey so they could send her back to the moment she was supposed to have died. However, as she was now effectively immortal, she decided that she had a small amount of "wiggle room" and would travel to Gallifrey "the long way 'round" and could "stop off along the way". This TARDIS later passed the Doctor's whilst both moved through open space. (TV: Hell Bent)

Later developments
Me and Clara were travelling in their TARDIS when Clara was compelled to return to Nevada in temporally-abnormal circumstances and met the Doctor during his travels with Bill Potts. After joining the Doctor on an expedition to the Underhenge, Clara parted ways with him again and returned to the diner TARDIS. Standing in the "diner" room, the two women agreed to try and disentangle themselves from the Doctor's timeline, and, to do so, set a course for the most boring place Me knew, and thus the least likely to be visited by the Doctor: the Minyan ship. (GAME: Lost in Time)

Me and Clara were later joined on their travels by Willa Twiston. (PROSE: The Witchfinders)

During his last talk with Clara before she took off, the Twelfth Doctor realised that the diner was the same one where he'd once met Amy Pond and Rory Williams (TV: Hell Bent) in 2011 during the event surrounding the Eleventh Doctor's supposed "death" at Lake Silencio. (TV: The Impossible Astronaut) The Twelfth Doctor was confused by the different location, not having yet realised the diner was TARDIS. (TV: Hell Bent)

Behind the scenes

 * The interior of Clara's TARDIS is a near-replica of the TARDIS set used during the First Doctor's era. The console is identical, although painted white (in the original production of the series, the interior was green in the real world to give-off a more bright impression on-screen. Indeed, in-universe the interior of the TARDIS was meant to be pure white).
 * The diner scenes are in fact filmed in the same real-world diner as the one in The Impossible Astronaut, to which the Doctor alludes: Eddie's Diner, in the Cardiff Bay area.
 * The TARDIS' undisguised form is reused on the cover of Time War: Volume Three, suggesting it is either a Type 50 or Type 55.