Compassion

Compassion was originally a woman called Laura Tobin, who was part of the original colony on Anathema. She, like all the colony residents, either was or became sterile. They therefore reproduced using Remembrance Tanks, and over the millennia that the ship that Anathema was based upon took to get to Earth, all the colonists were remembered using biomass inside the remembrance tanks. Compassion is the result of this process. (EDA: Interference - Book Two)

Compassion was a member of the Remote, an offshoot of Faction Paradox. Following her encounter with the Doctor on Earth she chose to travel with him and Fitz (whom she / Laura Tobin once knew, she also knew Kode who was the remembered version of Fitz).

As Compassion came from a media / signal orientated culture she always wore an ear piece (or receiver), The Doctor interfaced her receiver with the TARDIS systems to protect her from any 'harmful' signals she might encounter during their travels.

This interface had unforeseen results, warping her biodata along Block Transfer Computations, culminating in her 'birth' as a sentient TARDIS. (EDA: The Shadows of Avalon)

The Time Lords pursued her, the Doctor and Fitz travelling within her, eventually leading to their forced arrival on Gallifrey just before the Faction Paradox attack, and Gallifrey's eventual destruction.

After the destruction of Gallifrey, she dropped off the Doctor on 19th century Earth, dropped off Fitz Kreiner on 2001 Earth, and left to explore the Universe with Gallifreyan technician Nivet. (EDA: The Burning, Escape Velocity)