Former Lord President

Former Lord Presidents, informally called ex-presidents, were individuals who previously served as the President of the High Council on Gallifrey. They were sometimes given special rights different from other Time Lords under Gallifreyan law because of their previous position. (PROSE: The Eight Doctors, AUDIO: Mindbomb)

Powers
Some former Lord Presidents were entitled to retain their place on the High Council. Acting President Flavia, who resigned to formalise her position by way of an election but lost to Niroc, remained on the Council but was isolated from the Inner Council and other members as Niroc's grip on them grew.

Former presidents were also entitled to set up a presidential inquiry overseen by a Committee of Enquiry (PROSE: The Eight Doctors) as well as judicial inquiries. (AUDIO: Appropriation) The Sixth and Eighth Doctors set up an inquiry into the former's trial on Space Station Zenobia. (PROSE: The Eight Doctors) Romana II set up an inquiry into her impeachment which ended in the High Council technically recognising her presidency by motioning a vote of no confidence. (AUDIO: Appropriation)

Some Presidents had no rights after their terms had ended. For example, Pandora and Morbius were both condemmned to death. (TV: The Brain of Morbius, AUDIO: Lies) Other presidents had their terms ended due to their own deaths meaning they served no time at all as ex-presidents. (TV: The Deadly Assassin, PROSE: The Ancestor Cell)

Other references
During the Sontaran Temporal Offensive, Svild was informed that the Doctor, former President of Gallifrey, was in the Crimea; he had infact been told this by the Thirteenth Doctor. (TV: War of the Sontarans)