Earlier race of Time Lords

Some accounts suggested that the "group of beings" who survived the destruction of their own universe, which existed before the creation of the Doctor's universe in the Big Bang, and became the Great Old Ones (PROSE: All-Consuming Fire) or elder gods, were originally an "earlier race of Time Lords", the Time Lords of that universe just as the Doctor's people were the Time Lords of their own reality. (PROSE: Millennial Rites, Divided Loyalties) Though they would have called themselves Time Lords as well in their original reality, the Doctor only called them such in quotation marks, as they had been Lords of "a very strange version of time and space" indeed. (PROSE: Millennial Rites)

"In the dying days of the universe before this current one, which is forever separated from us by a point where time and space do not exist, a group of beings discovered how to preserve themselves past that point where their universe ceased. They shuttled themselves sideways, into a parallel universe which, for various reasons that I will not even attempt to explain now, ceased a split-second after our one. (…) Just before that universe ceased, they jumped back to our one, which had just started expanding afresh after a moment of nothingness. The trouble is, the universe before ours was set up differently. Fundamental physical laws such as the speed of light and the charge on the electron were different, which means that the Great Old Ones have powers undreamed of by anybody in this universe. Powers that make them look like gods, to naive races."

- Seventh Doctor (PROSE: All-Consuming Fire)

Yog-Sothoth, later known as the Great Intelligence, was the military strategist of these "Time Lords". Others of this race, reborn in monstrous bodies made of pure energy which couldn't fully exist in three-dimensional space included Lloigor, whom the Doctor identified as (PROSE: Millennial Rites) the Animus of Vortis, (TV: The Web Planet) and Shub-Niggurath, whom the Doctor identified as the mother of the Nestene Consciousness on the planet of Polymos. Yog-Sothoth stayed in contact with them, and they mocked him for his lack of success with the "war games" he played in various planets in the universe, including (PROSE: Millennial Rites) his attempts to conquer Earth using Robot Yeti. (PROSE: Millennial Rites, TV: The Abominable Snowmen, The Web of Fear)

According to one account, Rassilon studied these interlopers, coming to suspect their origins as the Time Lords of another, destroyed reality. He was the one who named them "Great Old Ones", and also gave them individual names to give future Time Lords power over them. In addition to Yog-Sothoth, Loigor and Shub-Niggurath, his list included Hastur, (PROSE: Divided Loyalties) whom the Seventh Doctor stated was the true identity of his enemy Fenric, (PROSE: All-Consuming Fire) as well as Cthulhu, (PROSE: Divided Loyalties) identified by the Seventh Doctor as the Old One he had fought in 1915 Haiti, (PROSE: All-Consuming Fire, White Darkness) Tor-Gasukk, Gog and Magog, Nyarlathotep, Dagon, and Melefescent. (PROSE: Divided Loyalties) He also cited the three Gods of Ragnarok, Raag, Nah and Rok, whom he believed responsible for the destruction of the Old Ones' original universe.

Additionally, Rassilon wondered if the Guardians of Time were simply powerful Great Old Ones, or an even greater, more primordial class of entity. The Black Guardian and White Guardian refused to answer when he met them, but the Sixth Doctor later believed the Guardians to indeed be the "upper echelons" of the Great Old Ones from the old universe, something he repeated to another Guardian without being contradicted. (PROSE: Divided Loyalties)

Behind the scenes
Craig Hinton provided BBC Books with worldbuilding notes on the cosmology he was using in The Quantum Archangel, which were later published in the charity anthology Shelf Life. These notes elaborated on his views regarding the Great Old Ones' universe and its Time Lords, referred to therein as "the Old Time Lords". These notes included the idea of the Guardians of Time as other survivors of the old universe, as also established by Gary Russell in Divided Loyalties.

"When the last universe collapsed, a number of Time Lords made the transition as well. These are now known as the Great Old Ones (qv Lovecraft). They are unbelievably powerful, but some are more powerful than others. The High Council of the Old Time Lords were all linked to the Matrix when the universe ended. They became the Guardians – sentient life-forms that acted as the vessels or conduits through which the fundamental essence of the Universe could act."

- Craig Hinton

Specifically, the President of the High Council became the Black Guardian, the Chancellor became the White Guardian, the Castellan became the Azure Guardian, the Matrix Keeper became the Crystal Guardian (otherwise known as the Toymaker), "the Renegade" became the Red Guardian (who was the Other, and is thus the Doctor, who will revert to his true identity as the Red Guardian after reaching his final regeneration). Additionally, the Matrix itself became the Gold Guardian.

Hinton clarifies his usage of "the Transient Beings" (a phrase name-dropped in The Crystal Bucephalus and Millennial Rites) as referring to the lesser Old Time Lords, the ones whom Russell's Divided Loyalties would dub the Sub-Guardians, reserving the title of Great Old Ones for them.

"The other Time Lords (those not attached to the Matrix but within the bubble that surrounded their Gallifrey) became the "evil from the dawn of time" types, also known as the Transient Beings – Yog-Sothoth, the Time Lord military strategist, became the Great Intelligence; Lloigor, a Senior Watcher, became the Animus; Shub-Niggurath, that universe’s equivalent of the head of the CIA, spawned the Nestene Consciousness… and so on. Importantly, none of them has any memory of the previous universe. All they want to do is conquer. Over time, they have built up a rivalry between themselves. Fenric and the like… But there are others."

- Craig Hinton

Despite also citing him in this passage (in accordance with his identification as one of the Hinton-compliant Great Old Ones in Andy Lane's All-Consuming Fire), another part of the Notes specifically disregarded the idea of Fenric/Hastur being one of the Great Old Ones/old Time Lords, instead harkening back to his explanation in The Curse of Fenric itself as a manifestation of the primordial evil of this universe; in fact, he was depicted as the incarnation of Anti-life, the natural, antimatter-style counterpart of "the Life of the Universe (not to be confused with the 'essence of the Universe' that the Guardians represent)".

The notes also clarified that the Gods of Ragnarok were not members of this earlier race of Time Lords, but actually twice removed: they were once one half of the High Council of the prior universe, alongside the off-screen "Gods of Armageddon". Surviving in the same manner into the Great Old Ones' universe, they acted as its equivalents of the Guardians of Time. "Raag, Nah and Rok were three of the Guardians of the previous universe, and they helped to bring that crashing to a close in a final great war involving their version of the Key to Time and that universe’s equivalent of the Daleks – not too dissimilar to the great war that was facing the Time Lords in our universe (until The Ancestor Cell). (…) Arma, Gedd and Onn [have] never [been] mentioned. But the other three guardians from the previous universe must have gone somewhere… Worth remembering for a future novel. However, powers and motivation will have to be very different from anything else. And one of them must be their version of The Renegade…"

- Craig Hinton