War prediction

War predictions were predictions of the destruction of Gallifrey in a war. Despite the Time Lords being unable to observe their own future due to the Protocols of Linearity, throughout their history, multiple parties were able to guess at Gallifrey's future. (PROSE: The Gallifrey Chronicles, The Book of the War)

Matrix 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)

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 Hybrid
In 2002, Sam Jones told Griffin about a Gallifreyan prophecy concerning a hybrid. She said the Doctor was a hybrid, his father a Time Lord and his mother a human, and that he was destined to unite the two races and "bring good old human niceness into their alien society". Though she thought she was bluffing to stall Griffin, the Eighth Doctor later asked her who had told her about the prophecy. (PROSE: Unnatural History)

The Twelfth Doctor later revealed that a legend on Gallifrey told that all prophecies in the Matrix concurred that the Hybrid of two warrior races would conquer Gallifrey and stand over its ruins before unraveling the Web of Time, destroying a billion billion hearts to heal its own. He went on to say, "The Hybrid is me." Ashildr suggested that the Doctor was the Hybrid because he was half-human. (TV: Heaven Sent, Hell Bent)

The Imperator
After ten 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)

The Order of the Weal
The Imperator founded the Order of the Weal to be run by his friend and disciple Chatelaine Thessalia. (PROSE: Return of the King) Though the Order eventually turned on the Imperator, Thessalia used it as a vessel for her own plans and preparations. She believed that the Homeworld'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. (PROSE: The Book of the War)

Greyjan the Sane
Greyjan the Sane was the shortest-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)

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 and become War Queen of Gallifrey. 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 centred 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) Shortly thereafter, a war broke out. The Watchmaker said this war would inevitably end in the destruction of Gallifrey. (AUDIO: Enemy Lines)

The War King
The Rivera Manuscript was written by a renegade of the Great Houses, translated by a human hand, and passed through the ownership of Diego Rivera, Jorge Luis Borges, and Salvador Allende before finding its way to the Eleven-Day Empire. The manuscript 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.

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

When the enemy invaded the Homeworld, the prophecy of the Rivera Manuscript was avoided thanks to the defenses that the War King had prepared. (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) Christine Summerfield visited the ruins of the Homeworld. (PROSE: Dead Romance) The planets New Alexandria and Ardethe were both hinted to be Gallifrey after the fall of Time Lord civilisation. (PROSE: The Crystal Bucephalus, Deadfall)

Lord President Umbaste effectively committed suicide by opening his biodata to the caldera, which was recognised 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 resurfaced over a year later, all he could say was the word "One", over and over again. The Book of the War said that he eventually committed suicide, (PROSE: The Book of the War) but Mr. Smith said that the secret minutes of House Dvora revealed who really killed Umbaste. (AUDIO: A Labyrinth of Histories)

Upon hearing rumours of a threat against Gallifrey, Irving Braxiatel planned a scheme to preserve the Time Lord biodata archive so he could reconstruct Gallifrey after its inevitable fall. (AUDIO: Panacea) After Braxiatel stopped Romana II from regenerating, saying her next incarnation had sent him to prevent a horrible war, the Watchmaker said that he needed to choose to remain on Gallifrey with the knowledge of what was to come, or to hide himself away forever. (AUDIO: Enemy Lines)

Entarodora expected the War to end either in the War being retroactively annulled or in one side's inexorable victory, upon which a new kind of history would be founded. Despite this, there were some brief attempts at peace, like the Venue Accords. (PROSE: The Book of the War)

The Accord foresaw a "great war spreading through time". They feared that the 1970s and 1980s, which had been temporally weakened due to the Doctor's frequent visits, would be damaged, so they tried to reinforce those decades by altering the time DNA of every person who lived through those decades so that they subconsciously realised that there were inconsistencies with history. (PROSE: The Enfolded Time)