C is for... Chancellery Guard

The internal security service of the Time Lords. They wore red uniforms with white trimmings, including a cloak. For weapons they used hand-held stasers. The Chancellery Guard acted as a form of police force on Gallifrey, and were called upon to add extra pomp at various ceremonies. In charge was a Commander, who answered to the Castellan - head of security and a member of the High Council. As the Doctor was a rebellious youth, he no doubt ran foul of the Chancellery Guard on numerous occasions prior to leaving Gallifrey. When he returned at the time of the Presidential resignation, his TARDIS' approach was detected and the Guard were sent to detain him, led by Commander Hilred. The Doctor gave them the slip, and Cardinal Borusa was annoyed that removing a number of Guards to hunt for him would diminish the resignation ceremony's spectacle. Once captured, and accused of assassinating the President, Hilred was authorised to torture the Doctor. The Castellan at the time was Spandrell. Hilred was later killed by the Master.
On his return to the planet, to claim the Presidency, the Doctor met Commander Andred. He was prepared to kill the Doctor to stop him collaborating with the alien Vardans who had invaded the planet. The Doctor was able to convince him that he was bluffing the Vardans until he could find a way to defeat them. Castellan Kelner was able to sow dissent amongst the Guard, with some of them killing those loyal to Andred. Once the Vardans, and then the Sontarans, had been expelled, the Doctor's companion Leela elected to stay behind and marry Andred.
Their next commander was the officious Maxil, who seemed to delight in persecuting the Doctor.
When all five of the Doctors were transported to the Death Zone on Gallifrey, the new commander was in league with President Borusa to frame the current Castellan, and he arranged his death in a staged escape attempt.
The Chancellery Guard were present at the Sixth Doctor's trial.

With the onset of the Time War, the Chancellery Guard became a more militarised force, with improved armoured costumes in a darker red, and with heavier weaponry. A more ceremonial version of the uniform retained the brighter red, with the white decoration - an armoured version of the original.

The Guard helped with the defence of Arcadia and the Capitol against the Daleks. When President Rassilon attempted to have the Twelfth Doctor executed, the Guards chose not to obey - many having fought alongside him in the war. They stood alongside him, leading to Rassilon's downfall.

Appearances: The Deadly Assassin (1976), The Invasion of Time (1978), Arc of Infinity (1983), The Five Doctors (1983), The Trial of a Time Lord (1985), The Day of the Doctor (2013), Hell Bent (2015).

• The 2013 anniversary prequel, The Last Day, focuses on the Chancellery Guard, employed to man Sky Trenches over Gallifrey.