President of the High Council

The President of the Supreme Council of Gallifrey and All Her Dominions, Holder of the Wisdom of Rassilon, Preserver of the Matrix, Guardian of the Legacy of Omega, often simply Lord President or Lady President, governed the High Council of Time Lords, making him or her the holder of the most powerful office on Gallifrey. (AUDIO: The Inquiry)

Prerogatives
The ceremonial privileges of the President included access to the APC Net by means of the Matrix Crown (TV: The Invasion of Time) and the possession of the Sash and Rod of Rassilon. (TV: The Deadly Assassin) Donning the sash also affected a permanent change to the biodata of the Time Lord who wore it as President, providing the Doctor and others with access to secret biodata codes that would grant access to some of the Time Lords' greatest and most powerful secrets (PROSE: Alien Bodies).

The President also had the formal responsibility, not attempted in reality except by the Fourth Doctor, to seek the Great Key of Rassilon — a separate artefact from the Rod of Rassilon, which was also sometimes referred to as the Key of Rassilon. (TV: The Invasion of Time)

The Lord President could not be put on trial, (TV: The Mysterious Planet) but he or she could certainly be called to give evidence in a judicial investigation. (AUDIO: The Inquiry)

When Romana II's presidency was impeached and she was nearly deposed, in her present incarnation she wasn't permitted to contest the presidency against Inquisitor Darkel and Lord Cardinal Matthias, but she said she would go under voluntary regeneration and contest it in her next incarnation. This didn't happen as she wasn't deposed. (AUDIO: Appropriation)

Holders of the office of president
Rassilon was the first President and founder of modern Time Lord society. (TV: The Five Doctors)

Pandak was one of the early Time Lord Presidents and one of the founders of Time Lord society. (PROSE: Lungbarrow, PROSE: The Ancestor Cell)

Pandora was the first female President. She was overthrown by her High Council after claiming the title of Imperiatrix. (AUDIO: Lies)

Morbius was a president who led a war of conquest. He was overthrown by the High Council. (TV: The Brain of Morbius)

Saran was Vice President, but became President during the Morbius Crisis. (PROSE: Warmonger)

Drall was President during the First Doctor's time at the Time Lord Academy. (PROSE: Divided Loyalties)

Pandak III ruled for over 900 years (TV: The Deadly Assassin)

Greyjan the Sane was President for three days between the 2nd September 1752 and 14th September 1752. (PROSE: The Ancestor Cell)

A male President, the grandfather of Pundat the Third, changed the Constitution of the Time Lords to enable the President to name his own successor. Pundat the Third himself was a corrupt President shortly before the Doctor's departure from Gallifrey. He, in turn, was succeeded by Slann, who was President at the time of the Doctor's departure from Gallifrey, and was assassinated by the Master. (PROSE: Birth of a Renegade)

According to another source, President Pandad VII ordered Irving Braxiatel, then Lord Burner, to burn "an old man" and "his granddaughter" from history. He disobeyed this order and the intended victims stole a TARDIS and fled Gallifrey. The very same day, President Pandad died when a power relay in his office overloaded; an inquiry headed by Braxiatel found that this was an accident. (AUDIO: Disassembled)

The Fourth Doctor was the 407th President, (TV: The Invasion of Time, PROSE: The Ancestor Cell) while the Fifth Doctor later became the 409th President (TV: The Five Doctors) before being deposed. (TV: The Trial of a Time Lord)

Borusa served as President after the Doctor resigned from his role (TV: The Invasion of Time, Arc of Infinity), but eventually fell from grace when the stress of his new position drove him insane, causing him to seek the secret of immortality from Rassilon. This ended when Borusa was turned into living stone by Rassilon (TV: The Five Doctors), but Borusa was eventually released when he assisted the Doctor in dealing with various political crises (PROSE: Blood Harvest, The Eight Doctors).

Although he attempted to evade his role as President, the Fifth Doctor was eventually forced to take on those responsibilities when several Time Lords discovered that Borusa had manipulated the political process so that his immediate subordinates in the High Council lacked the political or personal strength to pose any real threat to his own power, and those who might have been able to resist him had been discredited. As a relative outsider to the political process, the Doctor was chosen as the best candidate to provide the Time Lords with a stabilising influence as they attempted to rebuild their political process. In the course of his election, the Doctor learned that his fourth incarnation's time as President had been officially stricken from the record. After he had completed his political reforms, the Doctor chose to resume his travels after appointing a successor, his old companion Leela reminding him that he had chosen to fight for the underdog and resuming his efforts to help people with the power of Gallifrey behind him would turn him into the tyrants he had always opposed. (AUDIO: Time in Office)

Flavia was appointed as 'acting' President by the Fifth Doctor when he chose to depart Gallifrey, before being overthrown in favour of Niroc. Niroc was president during Operation Ravolox and the Sixth Doctor's (faked) trial. He was a puppet of the Celestial Intervention Agency. (PROSE: The Eight Doctors) Flavia was again President for a period, then challenged and beaten for presidency by Romana II, (PROSE: The Eight Doctors, Happy Endings) who was also president into her third incarnation. (PROSE: The Shadows of Avalon, The Ancestor Cell)

A male President served as interim president during Romana II's imprisonment by the Daleks, (AUDIO: The Apocalypse Element) and was involved in the affair of the Sirens of Time before it was erased from history. (AUDIO: The Sirens of Time)

Romana II and Pandora (inhabiting the body of Romana's first incarnation) both claimed the title of Imperiatrix when Darkel invoked a "right of challenge" for the Presidency. (AUDIO: Imperiatrix)

Valyes was acting President after the defeat of Pandora and the incapacitation of Romana II. He resigned and Darkel, Matthias and Romana each claimed the Presidency. (AUDIO: Appropriation)

Irving Braxiatel was President, but resigned almost immediately, having named his successor. (AUDIO: Mindbomb) Matthias saw Gallifrey almost destroyed by the Free Time Dogma Virus. (AUDIO: Mindbomb, AUDIO: Panacea) Romana II returned to office after Matthias' efforts in stopping the Dogma Virus forced him to resign. (AUDIO: Ascension)

Another male President ruled for a time, sending Straxus on a mission to World War I. (AUDIO: X and the Daleks)

Trey was president during the rise of the Adherents of Ohm (AUDIO: Intervention Earth) and another crisis where a new generation of Battle TARDISes needed to be built. (AUDIO: Luna Romana)

At the beginning of the Last Great Time War, Livia was President (AUDIO: Enemy Lines, Celestial Intervention), but resigned due to her not wanting to rule during war times. This led to a political battle between Romana II and Valerian, but after a video of Romana making a deal with the Dalek Emperor was uncovered, Valerian was elected Lord President. Rassilon was resurrected through Valerian, killing him in the process (AUDIO: Desperate Measures), to lead the Time Lords against the Daleks. (PROSE: Engines of War) He was still President towards the end of the War, (TV: The End of Time, PROSE: Engines of War) but was overthrown by the Twelfth Doctor when he returned home, due to his anger at Rassilon's roles in Clara Oswald's death and the horrors of the Time War. Once in charge of Gallifrey, the Doctor banished Rassilon for his crimes even though he had nowhere to go, as Gallifrey was located at the end of the universe. (TV: Hell Bent)

Following Rassilon's banishment, the Twelfth Doctor became Lord President of Gallifrey himself, banishing the High Council as his first acts. However, this was all a ruse in order to gain access to a Time Lord extraction chamber to save Clara's life and he fled Gallifrey soon afterwards in a stolen TARDIS, once more abandoning the title of Lord President. (TV: Hell Bent) A female President succeeded the Doctor, inheriting Rassilon's gauntlet, but her reign was cut short when Gallifrey was invaded by Cybermen led by Rassilon, who killed her with a staser before reclaiming his gauntlet and title of Lord President. Due to the Doctor and Rassilon reversing these events, this President was restored to life. (COMIC: Supremacy of the Cybermen)

Other presidents included Pandat VII, (AUDIO: Disassembled) yet another male President, (TV: The Three Doctors) and an assassinated male President. (TV: The Deadly Assassin)

Alternative timelines
In an alternative timeline, the Doctor became Lord President and led the Time Lords in a war against the Daleks, who were being aided and abetted by the Master. (PROSE: The Quantum Archangel)

In a timeline in which it was standard policy for the Time Lords to sell their temporal technology to the highest bidder and regenerations could be extracted and sold, Leela and K9 Mark I accompanied the Fourth Doctor on his search for the Key to Time. She was the only human to hold the Key to Time in her hands. Consequently, when Leela's counterpart from the proper timeline visited this alternative Gallifrey, she was appointed Lady President. (AUDIO: Reborn)

In a timeline in which the Time Lords regularly altered history through the Temporal Intervention Agency, Romana II became Lady President as in the proper timeline but was considerably more ruthless than her counterpart. Her Interrogator General was Leela, who murdered her predecessor Narvin to achieve the position, while the Doctor, by then in his sixth incarnation, served as Lord Burner, the President's personal temporal assassin who "burned" people from history. Vansell served as Castellan. (AUDIO: Disassembled)

In a timeline in which Rassilon failed to finish the Eye of Harmony before his death, Romana II reigned as Lady President over a Gallifrey which never achieved time travel and where slavery still existed. She was assassinated on the orders of Lord Chancellor Narvin but was immediately replaced by her counterpart from the proper timeline, who claimed that the victim of the assassination was a decoy. After the alternative Narvin was killed by the Krilig, the Narvin from the proper timeline assumed his identity. (AUDIO: Forever)

In an alternate timeline in which the Daleks were peace-loving academics and friends of the Time Lords, a Lord President was cured by Dalek surgeons who removed a microaneurysm from his brainstem. (PROSE: The Ripple Effect)

In an alternate timeline in which the Doctor never left Gallifrey, Susan Foreman ran for the presidency. (AUDIO: Auld Mortality) She won the election after the Doctor left Gallifrey. (AUDIO: A Storm of Angels)

The Infinity Doctors universe
Voran, Dromeian Castellan was acting President in one universe. (PROSE: The Infinity Doctors)

Presidente de Gallifrey