Gallifrey's time stream

Gallifrey existed in both N-Space and an exclusive time stream separate from the rest of history. This granted the Gallifreyans higher power over time, but came to have drawbacks as Gallifrey's history progressed. Romana II believed that this made the planet a temporal anomaly, (PROSE: Lungbarrow) but The Book of the War indicated that this enclave of the continuum made the planet the very core of history. (PROSE: The Book of the War)

Nature
Romana indicated that this exclusive time stream existed long before the Time Lords, giving the ancient Pythia a sensitivity towards time and its movement. (PROSE: Lungbarrow) Ancient Gallifrey contained the Crevasse of Memories That Will Be, the chasm through which time was poured into the universe by its Goddess. The Pythia got their powers from the Crevasse, (PROSE: Cat's Cradle: Time's Crucible) suggesting it to be the time stream's source. (PROSE: Lungbarrow)

Omega credited himself with his people's development of time travel and maintained that, without him, the now Time Lords would still have been "locked" within "[their] own time". (TV: The Three Doctors) Indeed, in one version of reality glimpsed by Omega, the Time Lords became "gods" thanks to him as there was no Rassilon at all. (PROSE: The Infinity Doctors)

Following the Pythia's fall, Rassilon brought the Eye of Harmony to Gallifrey to give the planet a powerful stability. However, the Eye's stability (PROSE: Gallifrey - Notes on the Planet's Background) slowed down the time speed "metabolism" of Gallifrey's time stream in relation to the wider Universe, making it like "a clock that's losing perhaps a second every hour and [is] getting slower all the time." (PROSE: Lungbarrow) In Auld Mortality's universe, the Doctor said that Earth was different from Gallifrey because it had an ongoing history. (AUDIO: Auld Mortality)

Contrary to some of the above details, The Book of the War described the Homeworld's exclusive space and time of its own as being created during the anchoring of the thread, when the planet removed from the Spiral Politic and re-engineered into a biodata-enabled receiver and processor of information, becoming the central node of history. (PROSE: The Book of the War)

The Doctor's time stream followed that of their home planet to the point that the Thirteenth Doctor observed that, in "[her] time", Gallifrey was "forever" gone after finding it had been razed by the Spy Master. As such, when she encountered Gat and an unfamiliar incarnation of herself on Earth in 2020, she concluded that the two Gallifreyans must have been from the past relative to her. (TV: Fugitive of the Judoon)

In the time of the Infinity Doctor, the timezone in which the Time Lords lived was around 10 billion years after the creation of the universe. (PROSE: The Infinity Doctors)

Time War and beyond
Following his first regeneration during the Last Great Time War, claimed that the "Time Lords [stood] outside space and time and look[ed] upon their realms as a god look[ed] down on creation". He dismissed the Daleks as "microbes" who were "tied to one timeline, to limited dimensions". The Dalek Emperor decried this as "blasphemy" and claimed that it was the god emperor of the universe. (AUDIO: Homecoming)

Within the war, the Time Lords were aware that they were time locked in "another version of reality". (PROSE: Dalek Combat Training Manual, TV: The End of Time) The war ended in the so-called fall of Gallifrey, in which all incarnations of the Doctor saved Gallifrey by relocating it to a parallel pocket universe. (TV: The Day of the Doctor)

Following the Siege of Trenzalore, the Time Lords returned Gallifrey to the universe, (PROSE: A Brief History of Time Lords) through a manner the Doctor purposefully did not try to find out, in order to not make the other Time Lords "feel clever". In doing so, the Time Lords displaced Gallifrey in time, and it now existed at "the end of the universe". This was ultimately discovered by the Twelfth Doctor. (TV: Heaven Sent, Hell Bent)

The Spy Master, however, recalled to the Thirteenth Doctor that Gallifrey was still "hiding in its little bubble universe" when he returned and ravaged the planet in retaliation for the secret of the Timeless Child, which the Time Lords had kept from him and the Doctor. (TV: Spyfall)