Lord Cardinal

A Lord or Lady Cardinal (also known simply as Cardinal) was the highest-ranking member of a Chapter on Gallifrey. As such, they were entitled to sit on the High Council. (TV: The Deadly Assassin) 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
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 Borusa 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)

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
Borusa was a Cardinal when the President was assassinated by Goth. (TV: The Deadly Assassin)

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)

Both Ollistra (AUDIO: Only the Monstrous, The Side of the Angels) and Padrac (AUDIO: The Eleven) were Cardinals during the Doom Coalition crisis. Ollistra continued as Cardinal through into the Time War.

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)

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) were all Cardinals at one point.

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)

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