Second Time Lord

The titles of First Time Lord, Second Time Lord and Third Time Lord referred to "the three most superior Time Lords".

A First, Second and Third Time Lord formed the High Tribunal (PROSE: Doctor Who and the Doomsday Weapon) who sentenced the Second Doctor to his exile on Earth. The Second Time Lord present during these events, (TV: The War Games) Councillor Adelphi, (PROSE: The Legacy of Gallifrey) still held the title, now in a new incarnation, when he and the other two pondered what to do about the Doomsday Weapon crisis. (TV: Colony in Space, PROSE: Doctor Who and the Doomsday Weapon) In-between these events, 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)

Behind the scenes
Originally, the Time Lord Chancellor in The End of Time was to be credited as as "The Second".