Second Time Lord (The War Games)

In one incarnation, a Second Time Lord was one of the three Time Lords who held the trial of the Second Doctor.

At the trial
This Time Lord, Councillor Adelphi, was assigned to be part of the tribunal on orders of Lord President Pandad IV as a direct result of Rassilon's agent, Socra, being asked by his Matrix Lord masters to keep an eye on the Doctor. (PROSE: The Legacy of Gallifrey)

Adelphi was a member of the High Council, in addition to serving on the tribunal that sentenced the Doctor. (PROSE: Doctor Who and the Terror of the Autons) Adelphi had been sent to the tribunal on orders of Lord President Pandad IV as a direct result of Rassilon's agent, Socra, being asked by his Matrix Lord masters to keep an eye on the Doctor. (PROSE: The Legacy of Gallifrey)

The First Time Lord, Second Time Lord and Third Time Lord captured the War Lord after being alerted to his plans by the Second Doctor's Hypercube. He personally explained what the War Lord and his people had done, and how his plans were "an utterly callous disregard for the lives of the humans involved, and for the liberties of all the other species in the galaxy." When he asked the War Lord if he had anything to say in his defence, the War Lord refused to say anything. The Second Time Lord used some of his power to cause intense pain for the War Lord until he spoke, saying that the Doctor collaborated with the War Chief, and that the Doctor was guilty too for it.

The Second Time Lord then sentenced the War Lord to dematerialisation, wiping him out of existence after his verdict of guilty was reached, before listening to the Doctor's defence when his own trial came up and listened as the Doctor passionately addressed the Time Lords' own non-intervention policy and saying they should be helping those in need much like he did. The Second Time Lord later witnessed the Doctor refuse each new appearance offered to him when he and Goth announced his punishment for breaking the Laws of Time was an exile on Earth and a forced regeneration. (TV: The War Games)

Later incarnations
The Time Lord messenger who warned the Third Doctor about (TV: Terror of the Autons) was a new incarnation of one of the Time Lords at his trial, (PROSE: Doctor Who and the Terror of the Autons) and was identified in the Scrolls of Gallifrey as distinct from the First and Third, placing him as yet another incarnation of Adelphi. (PROSE: The Legacy of Gallifrey)

The same Second Time Lord who had belonged to the "High Tribunal" sentencing the Second Doctor (PROSE: Doctor Who and the Doomsday Weapon) was still the holder of the title, in a new incarnation, during the Doomsday Weapon crisis. (TV: Colony in Space)

Behind the scenes

 * Some time after he played "Time Lord 2", Trevor Martin played another, much more illustrious Time Lord off-screen: the Doctor himself in a new incarnation, first debuted in the play Doctor Who and the Daleks in Seven Keys to Doomsday and reprised the role in its audio drama adaptation. The play was first performed in a theatre venue called the Adelphi, hence the name given to Martin's earlier Doctor Who character by Gary Russell.
 * In the parallel universe setting of Exile, the court's place is taken by a pair of Time Lords, with Time Lord 2 being voiced by David Tennant.