War prediction

Though they had power over all of time and space, due to the Protocols of Linearity, Time Lords were incapable of directly observing their own future. However, throughout their history, multiple parties predicted the destruction of Gallifrey in a time war. These were collectively known as War predictions. (PROSE: The Gallifrey Chronicles, The Book of the War)

Prophecy
The generation of Time Lords before the Doctor's amassed enough information to glean something of their future. They knew that a spate of attacks would strike Gallifrey, one by one. These would include Omega, the Sontarans, Tannis, Faction Paradox, Varnax, Catavolcus, and the Timewyrm. A single Time Lord would be central to all these events, and Gallifrey would survive each attack. (PROSE: The Infinity Doctors, The Gallifrey Chronicles)

However, Gallifrey would nevertheless fall in a war against an implacable enemy, who would be unknown until Last Contact was made. Then, the one Time Lord would find the Lost Scrolls of Rassilon and lead Gallifrey from the darkness.

The president and members of the Supreme Council knew this prophecy, but they kept it hidden, fearing that Gallifrey would fall into chaos if it was widely known. (PROSE: The Gallifrey Chronicles) The council was split on whether to tell the Matrix to look for threats matching the description, since such action might inevitably lead to contact and conflict with the enemy. Deliberation on the topic took several millennia.

The Doctor was aware of this prophecy. (PROSE: The Infinity Doctors) His student Larna shared it with Ulysses, Penelope Gate, and Saldaamir at the Shoal. (PROSE: The Gallifrey Chronicles)

The Imperator
After millions of years of stasis on the Homeworld, inexplicable anomalies appeared in the breeding engines. This was interpreted by some as the Homeworld's acausal reaction to the events-to-come. (PROSE: The Book of the War)

The Imperator was one such anomaly, and he pushed for the Great Houses to drop their non-interventionist policies and become involved in the outside universe in preparation for an inevitable upcoming conflict. He also founded the Order of the Weal, run by his friend and disciple, Chatelaine Thessalia. (PROSE: The Book of the War, The Return of the King)

Though the Order of the Weal eventually turned on the Imperator, Thessalia used it as a vessel for her own plans and preparations. She believed that Gallifrey's enemy would be motivated unambiguously by a racial-survival agenda and mainly concerned with maintaining the integrity of its own history. She also expected the first attack on the Homeworld to be aimed at its noosphere, with physical fighting only occurring in the final stages of the war. In anticipation of this, she commissioned the babels as a defense for the Homeworld's noosphere. (PROSE: The Book of the War)

Greyjan the Sane
Greyjan the Sane was the shorted-reigning President of Gallifrey. Before becoming President, he researched the patterns of time. He believed that a law like chaos theory governed paradox. This research led him to foresee the War, and he invented a plan for creating backup Gallifreys. He was publicly perceived as a prophet of doom.

He also researched the origins of life. Observing the common physical and chemical characteristics of all life, he theorized all living things in the universe were descended from a single "ancestor cell". However, before that cell, other organisms existed with exotic and alien biochemical systems, and by feeding off TARDIS pollution and the energies of temporal paradox, these cells would be able to grow into life that was impossible for the Time Lords to fathom and utterly inimical to their existence, which would eventually destroy Gallifrey. This theory drove him to suicide after only three years in office.

After his death, his sciences were outlawed and declared arcane, though Romana III would later build his Nine Gallifreys. (PROSE: The Ancestor Cell)

Doom Coalition
When Padrac became Lord President and gained access to the Matrix, he saw that in every projection of Gallifrey's future, the Time Lords were destroyed by war, attrition, or collateral damage in the battles of other species. The only scenario in which Gallifrey survived was the one where the Time Lords were the only race in the universe. To achieve this, Padrac founded the Doom Coalition, who planned to use the Crucible of Souls to convert all the universe's energy into regeneration energy, making the Time Lords immortal while destroying the universe. (AUDIO: The Crucible of Souls)

The Rivera Manuscript
The Rivera Manuscript was written by a renegade of the Great Houses, translated by a human hand, first recorded as belonging to Diego Rivera, and distributed through the twentieth century to Jorge Luis Borges to Salvador Allende to the Eleven-Day Empire. It told of the narrator's imprisonment by an unknown power and the results of his forced exposure to a high dosage of praxis. The account seemed to predict the enemy's first invasion of the Homeworld, or at least a version of the Homeworld where the War King never prepared the Great Houses. (PROSE: The Book of the War)

Romana
After the Doctor rescued Charlotte Pollard and began the anti-time infection of the Web of Time, the Matrix started to break down. Upon entering its projection of the future, the Doctor saw a Gallifrey choked with smog and ruled by Imperiatrix Romana. The planet was part of "the empire of Zagreus", engaged in a ruthless five-dimensional war against any perceived threat to the Time Lords' supremacy. (AUDIO: Neverland)

After the Doctor visited the Enclave, (PROSE: The Blue Angel) the Time Lords began monitoring the war there and noticed reflections of a conflict in their own future. This drove Romana to regenerate into a harsher incarnation. She created the Nine Gallifreys and instructed her servants to seek out and capture Compassion with brutal means because she knew that Gallifrey would use type 103s in their future. (PROSE: The Shadows of Avalon)

During Romana's final term, an anomalous singularity appeared centered around Earth. It grew exponentially, draining energy from the universe around it and twisting space-time out of shape. The pre-cogs, Time Lords who channeled the timelines to predict Gallifrey's future, began to see the same future in every timeline: a future where Gallifrey had fallen and the Time Lords had never existed. (AUDIO: Intervention Earth)

The War King
The Homeworld's most infamous criminal and renegade surrendered himself to the Homeworld to tell the then-President his knowledge about a future enemy. The President didn't believe him, so five years later, the renegade returned and addressed a Closed Session of the Ruling Houses, warning them about an upcoming war. They pardoned him of his crimes, but the Presidency was still in denial, so he left the Homeworld to prepare defenses, only returning forty years later. The ensuing drama with the Faraway Declaration culminated in his promotion to. He immediately took action, appointing the first Academician for Game Logic and commissioning the 90-form timeships, though he only officially became the Homeworld's War King several years later. (PROSE: The Book of the War)

Miscellaneous
Frightened at the prospect of war, the Celestial Intervention Agency preemptively removed themselves from time, becoming the Celestis. (PROSE: Alien Bodies)

Ruath foresaw that there would be no sign of civilisation on Gallifrey by the 20th century. (PROSE: Goth Opera)

President Umbaste effectively committed suicide by opening his biodata to the caldera, which was recognized as a potential way to gain insights into future events. It launched him into a fugue state, his body just a husk while his mind traveled through the meta-structure of history. When he eventually resurfaced, over a year later, all he could say was the word "One", over and over again. (PROSE: The Book of the War) When Cousin Shuncucker burned down the records library in the Great Houses' prison planet, Mr. Smith said that no one would be able to know the truth behind Umbaste's alleged suicide. (AUDIO: A Labyrinth of Histories)

Upon hearing rumours of a threat against Gallifrey, Braxiatel planned a scheme to preserve the Time Lord biodata archive so he could reconstruct Gallifrey after its inevitable fall. (AUDIO: Panacea) Later, he rescued Romana II from regenerating, saying that a war broke out sometime after the return of Omega. (AUDIO: Enemy Lines)