Flavia has been described as High Chancellor, which might be a better name in terms for gender neutrality.
Talk about it here.
The Chancellor was next in rank to the Vice President, and so third in the overall hierarchy. As there often was no Vice President, the Chancellor would rank directly below the Lord President. (TV: The Invasion of Time)
The appointment of the Chancellor was in the hands of the President. (AUDIO: Pandora) However, during the sede vacante of the Fourth Doctor as a President-elect, not yet invested, the High Council ratified the appointment of Borusa as Chancellor. (TV: The Invasion of Time) In another occurrence, President Romana II allowed the Council to appoint Valyes acting Chancellor after Braxiatel was removed from office. (AUDIO: Insurgency)
Other information Edit
By the time of the run-up to the War, there appeared to be four Chancellors: the Chancellor of Time Past, the Chancellor of Time Present, the Chancellor of Time Parallel, and the Chancellor of Time Future. (PROSE: The Ancestor Cell)
Known holders of the office of Chancellor Edit
Known holders of this office included Slann, (PROSE: Birth of a Renegade) a male chancellor, (TV: The Three Doctors) Delox, (PROSE: Divided Loyalties) Goth, (TV: The Deadly Assassin) Borusa, (TV: The Invasion of Time) Thalia, (TV: Arc of Infinity) Flavia, (TV: The Five Doctors) Theora, (PROSE: Lungbarrow) Braxiatel, (AUDIO: Pandora) Valyes, (AUDIO: Insurgency, Fractures) the Chancellor, (TV: The End of Time) and, on an alternate Gallifrey, Narvin. (AUDIO: Forever)