The First Drax was a renegade Time Lord that knew the Doctor before either had left their home planet of Gallifrey.
Biography
Like all Time Lords, Drax was taken from his family at the age of eight for the selection process in the Drylands. Staring into the Untempered Schism as part of a Time Lord initiation rite, Drax reacted by running away from what he saw in the Schism. (PROSE: A Brief History of Time Lords)
Drax attended the Prydonian Academy with the First Doctor in the Class of 92. They took the tech course together. Though his practical work was satisfactory, he failed his exams, done in by temporal theory. (TV: The Armageddon Factor) Whilst he was at the academy, Drax became a member of the Deca and had his own self-made skimmer. At some point Drax escaped Gallifrey, after purchasing his own TARDIS. (PROSE: Divided Loyalties)