Matrix Lord

The Matrix Lords were the disembodied minds of deceased Time Lords as they existed within the Matrix. With their mental powers growing to immense length, and further boosted by their Amplified Panatropic Computation Net, they exerted an influence over physical reality greater than they ever had in life, and ruled the living Time Lords from behind the scenes via the Celestial Intervention Agency. (PROSE: The Legacy of Gallifrey)

The minds within the Matrix were even more conservative and dismissive of change than living Time Lords. (AUDIO: Neverland)

Some Matrix Lords were the Gallifreyan representatives amongst the High Evolutionaries. The primary Matrix Lords were Rassilon and his two aides, Morvane and Bedevere.

Rassilon declared the "council chamber" of the Matrix Lords and the High Evolutionaries as the home of the Celestial Intervention Agency. (COMIC: The Tides of Time)

In one possible reality, the Time Lords retreated into the Matrix when they were all killed by an alien race, leaving the pale aristocrat Ninth Doctor and the Master the only living Time Lords in the universe, where they were sent on dangerous missions by the Matrix-dwelling Time Lords. (PROSE: Doctor Who - The Ninth Doctor)