Lord Cardinal

A cardinal was a senior official of one of the six Gallifreyan chapters. (PROSE: Doctor Who and the Deadly Assassin) Each had multiple cardinals, who met as the Chapter Council. (PROSE: Lungbarrow) A number of cardinals, but not all, sat on the High Council. (AUDIO: Spring, Lies)

Related positions
The most senior cardinal was known as the Cardinal Prime. (PROSE: Lungbarrow) Somewhere between Under Cardinal (A sub office of Cardinal, ranking below it) and Cardinal, there was the rank of Junior Cardinal, a rank held by Borusa at the time of the Morbius crisis. They wore grey robes. (PROSE: Warmonger)

History
The First Doctor's family hoped that he would one day attain the rank of cardinal, making him the first of his House to do so. However, he had other plans for his future. (PROSE: Lungbarrow) His brother, Braxiatel, later became a cardinal. (AUDIO: Weapon of Choice)

Chancellor Goth told Castellan Spandrell that they would have to be quick to identify the arrival of a mysterious TARDIS as he had a meeting with the cardinals. (TV: The Deadly Assassin)

Chancellor told the Fourth Doctor that he would see what he could do to persuade the cardinals to accept him as President as politeness dictated. The Doctor pointed out that there were no other candidates and the cardinals need not be consulted. The Gold Usher welcomed them to the Doctor's investiture. (TV: The Invasion of Time)

By the time that the Time Lord Academy was opened to outsiders, the High Council was, according to Cardinal Braxiatel, made up of three cardinals who were unsympathetic towards President Romana. (AUDIO: Lies)

During the War in Heaven against the enemy, War Cardinals held a training facility on Gallifrey XII where they taught the art of escapology. (PROSE: Alien Bodies)

In an alternate timeline, the Cardinals served under a Supreme Pontiff of Time. (PROSE: Prisoners of the Sun)

Known cardinals
Cardinal was the leader of the Prydonian Chapter when the President was assassinated by Goth. (TV: The Deadly Assassin) He was later made Chancellor by the High Council. (TV: The Invasion of Time)

Braxiatel was a Cardinal and a confidante of President Romana. (AUDIO: Zagreus, Weapon of Choice, etc.)

Lenadi served as Cardinal Prime of the Prydonian Chapter on the High Council of Time Lords at the time of the First Doctor's disappearance from Gallifrey. (PROSE: Lungbarrow)

Matthias was Cardinal whilst Braxiatel was President, eventually succeeding him. (AUDIO: Appropriation)

During the Doom Coalition crisis, both Ollistra (AUDIO: The Side of the Angels) and Padrac were Cardinals. (AUDIO: The Eleven)

Valyes was a Cardinal who was chosen by the High Council as acting Chancellor. He replaced Braxiatel, who had been appointed to the position only days earlier. (AUDIO: Insurgency, Pandora)

Zero was a Cardinal, yet not a member of the High Council. (AUDIO: Spring)

Zorac was one of the Cardinals who sentenced the Fifth Doctor to death to stop Omega from taking over his body. (TV: Arc of Infinity)

Other cardinals included Franilla, Sendok, Zass, (PROSE: Divided Loyalties) Helron, Pandad, (COMIC: The Legacy of Gallifrey) Leabind, Tachen, (AUDIO: Lies) Luvis, (AUDIO: Omega) Morissa, (AUDIO: Lies) Tortheth (PROSE The Quantum Archangel) and Undercardinal. (AUDIO: Neverland)

One Cardinal wrestled with the Garvond in the Matrix. It ate away his remaining lives, killing him without hope of regeneration. This was recorded in The Worshipful and Ancient Law of Gallifrey. (PROSE: The Dimension Riders)

In one incarnation, Romana was Lord Cardinal of the Prydonian Chapter during Gallifrey's destruction. (PROSE: Lord Romanadvoratrelundar)

Cardeal