Gomer

Gomer was the Surgeon General of the High Council. He was a member of the Prydonian Chapter judging by his orange robes. Gomer was of strong enough character to argue with both Chancellor Borusa and the Gold Usher when the Doctor was apparently rejected by the Matrix. When the Vardans invaded Gallifrey, he was expelled from the Capitol as part of Kelner's grudge policy, to remove all those who had crossed him in the past. Gomer regarded Kelner with contempt. He joined Leela and the Outsiders when they formed a rebellion against the Doctor. (DW: The Invasion of Time)

It is probable that the Hospitaller on Gallifrey was the same person as the Surgeon General. When the Doctor returned to Gallifrey during his battle with Agonal, he entrusted an injured Tom Dekker to the Hospitaller, the latter gave his word as a Prydonian to do his best. (NA: Blood Harvest)