The term renegade Time Lord was an epithet applied by Time Lords against their fellows who went against Time Lord law. At various points, the Doctor was called and thought of himself as a renegade — but he also applied that label to others.
Alternatively, the term "ex-Time Lord" was applied to the Third Doctor. (COMIC: The Eternal Present) Many Renegades forsook their birth name and used titles, such as "the Doctor" and "the Master"; (PROSE: A Brief History of Time Lords) however, this practice was not exclusive to Time Lords working outside of the Gallifreyan orthodoxy, as evidenced by the Visionary (TV: The End of Time) and the General. (TV: Hell Bent) It could also be forced onto a Time Lord as a punishment, instead of being their own choice — as happened to the Woman. (PROSE: A Brief History of Time Lords)
Of the various reasons to call someone a renegade, none was more important than the simple act of physically departing Gallifrey. In this sense, the Seventh Doctor clearly thought of both himself and the Old Master as "renegades". There was, in this definition of the word, no connotation of any particular morality, since the Doctor and the Master had generally opposing value systems. (PROSE: The Novel of the Film)
To be labelled a renegade, it was enough to be a Time Lord not residing on Gallifrey, though in some cases a Time Lord could be responsible for some action the rest of the species found abhorrent. For instance, in the cases of two highly respected individuals, Hedin, a member of the High Council, betrayed Gallifrey by trying to aid the long lost Omega, (TV: Arc of Infinity) while the equally respected and renowned Ophiuchus conducted experiments designed to extend the Time Lord regeneration cycle. Accused of crimes such as vivisection, Ophiuchus was labelled a renegade. (COMIC: Ophiuchus)
Indeed, the hard choices involved in actually leaving Gallifrey were, according to the Fifth Doctor, a key distinction between a renegade and a mere "political rebel" still resident on Gallifrey. He felt that Ruath could have been a rebel, but not a renegade. (PROSE: Goth Opera) To leave Gallifrey forever was almost unthinkable to a Time Lord, given the very deep link between a Time Lord and their home-planet; orthodox Time Lords thought of leaving Gallifrey forever as a fate worse than death itself. Most Renegades harboured a secret hope of someday returning to Gallifrey. This was exhibited by Morbius after he became the General, (PROSE: Warmonger) as well as by the Doctor: as early as his first incarnation, the Doctor promised himself that he and Susan would come back "one day", (TV: An Unearthly Child) and the Eleventh Doctor came to believe that on some subconscious level, an eventual return "hom" to Gallifrey was "where [he'd] always been going" ever since he started running. (TV: The Day of the Doctor)
However, since Gallifrey had laws against interfering in the natural course of events, and leaving Gallifrey on un-sanctioned voyages typically led to interference, at least some segments of the Time Lord policy thought of renegades as definitionally criminal. For instance, when the Doctor was once accused of being a "dangerous renegade", Flavia instantly snapped to the Doctor's defence and pointed out that he wasn't a criminal. This immediately suggested that the word was commonly used to indicate criminality. (PROSE: The Eight Doctors)
Though the Doctor didn't himself feel that interference itself was illegal, (TV: The War Games) he did freely admit to interfering. Indeed, the Eighth Doctor felt that one definition of a renegade was a Time Lord who regularly picked up people on one world and transported them to another. (PROSE: Legacy of the Daleks) This implied that interference was part and parcel of being a renegade. On another occasion, the Eighth Doctor was pressed as to why he was a renegade. He simply said, "There are times when a little intervention is necessary." (PROSE: Interference - Book Two)
The legality of interference was debatable and the subject of several appearances in court for the Doctor. Out of his three known Time Lord trials, only one ended in conviction for interference. (TV: The War Games) The Sixth Doctor's trial ended in dismissal, (TV: The Ultimate Foe) while the Fifth Doctor escaped for unknown legal reasons, but not before being accused of playing too much cricket and essentially not interfering enough. (COMIC: The Stockbridge Horror) Even the Doctor's one conviction was hardly carried out with conviction. The Celestial Intervention Agency were only too happy to use the convicted Second Doctor to carry out their plans. (PROSE: World Game) Even the Third Doctor's so-called "exile on Earth" involved semi-regular contact with Gallifrey. (TV: Terror of the Autons, Colony in Space, The Curse of Peladon, The Mutants, The Three Doctors)
Thus, violation of the non-interference policy, while a frequent characteristic of the renegade, was simply not prosecuted consistently enough to be the determinative reason someone was labelled a renegade.
On still other occasions, other kinds of criminality engendered the use of the term. For instance, the First Doctor condemned Borusa as a renegade because his former teacher had broken any number of laws in his foolhardy search for immortality. (TV: The Five Doctors)
Renegades of the Great Houses could choose to undergo the Elective Semantectomy to remove their name from history and replace it with an epithet (like "the Hussar"). This was primarily performed as a way to protect the reputation of one's house and bloodline. (PROSE: Weapons Grade Snake Oil)
The first renegades were the Eremites.
According to The Book of the War, 1152 years before the start of the Great Houses' great time war against the Enemy, flaws were noticed in their breeding engines, though they were initially dismissed as "trivial". The generation of Homeworlders which grew from these flaws in the genetic looms included dangerous individuals who would go on to form the Homeworld's first batch of renegades. These included the War King, the Imperator and Grandfather Paradox. (PROSE: The Book of the War)
According to the Scrolls of Gallifrey, the first true Renegade Time Lord was Azmeal, who had been Rassilon's last confidant and the first High Chancellor of the newly-formed High Council. Forced to flee Gallifrey to escape from the jealous Lord President Helron after he gained a greater understanding of the Matrix than any other Time Lord, Azmeal hid out on a planet only for a mercenary warrior race hired by Helron to destroy it trying to get to him. Outraged at the senseless and uncaring violence of this act, Azmeal returned to Gallifrey and slaughtered Helron and his High Council. He was cautiously allowed to leave Gallifrey and continue his research at his leisure by the following High Council. (PROSE: The Legacy of Gallifrey)
Morbius was the cause of the Time Lords' great Civil War as he attempted to set up a rival Presidency; (PROSE: The Legacy of Galllifrey) although the Scrolls of Gallifrey had the Civil War predate Azmeal's betrayal by some margin, meaning Morbius would not be properly be a Renegade, (PROSE: The Legacy of Gallifrey) his trial was considered "the Trial of the First Renegade" by some historical records. (PROSE: Still Need a Title!) In the period between his exile from Gallifrey and his execution, he operated under the title of "the General" instead of his birth designation. (PROSE: Warmonger)
The Book of the War's account of the Imperator as a reformist, warmongering Time Lord president who was eventually executed via disintegration by the victorious Time Lords in an unprecedented move, which described the Imperator as one of the first generation of Renegades, (PROSE: The Book of the War) bore a startling resemblance to Morbius's campaign and downfall. The Doctor referred to Morbius as one of the very worst Time Lords, and knew his face on sight. (TV: The Brain of Morbius)
According to a Time Lord historian, the modern understanding of the term "Renegade Time Lord" referred to those who, for whatever reason, sought to leave Gallifrey following the passing of the non-interference policy. By the same source, the majority of those who fancied themselves as this and stole a TARDIS had short careers. Following these would-be Renegades being towed back to Gallifrey, they were punished by, ironically, being exiled from Gallifrey. (PROSE: A Brief History of Time Lords)
The Doctor, whose classmate the Master was later described as the worst of the Renegades Time Lord civilisation had produced, (TV: The Five Doctors) once encountered a version of Grandfather Paradox who was his own twisted future self. (PROSE: The Ancestor Cell) According to dreams the Fifth Doctor experienced about his youth, he, the Master, and fellow future Renegades the Monk, the Rani and Drax originally belonged to a clique known as the Deca at the Time Lord Academy, alongside Millennia and Rallon, the latter of whom became the incarnation of the Toymaker. (PROSE: Divided Loyalties)
The Scrolls of Gallifrey spoke of a generation of gifted but rebellious Time Academy students including the Doctor, the Master and the Rani, who engaged in anti-hierarchical behaviour due to a belief that no truer words had been spoken on the planet than Rassilon's last wisdom, about Time Lord society being set on a path of decay. (PROSE: The Legacy of Gallifrey)
Recalled to Gallifrey
The Doctor, despite being one of the more notorious Renegades, was used by the Celestial Intervention Agency (TV: The Two Doctors, PROSE: The Legacy of Gallifrey) and the Division as an often unwilling agent. (TV: Fugitive of the Judoon) This, and occasional offers to the Doctor to rejoin Gallifrey's society as no less than its Lord President, which the Doctor would always end up passing up on, (TV: The Deadly Assassin, The Five Doctors, The Invasion of Time) refusing to give up the "buccaneering life" for "anyone", (AUDIO: Doctor Who and the Pirates) as well as a one-time offer from the High Council to grant the Master a full pardon and a renewed regeneration cycle, (TV: The Five Doctors) were nevertheless nothing in comparison to the reliance the Homeworld would come to have on Renegades as it abandoned peace and engaged once more in bloody time warmongering.
Leading up to the War in Heaven, Gallifrey's most infamous repeat-offender, (PROSE: The Book of the War) a distinction other accounts attributed to the Master, (TV: The Five Doctors, The End of Time) returned to the Homeworld with prophecies of War and the Enemy, and cowed the Houses into making him the War King of the Homeworld after the previous Head of the Presidency was killed by the Enemy while engaged on an ill-fated crusade to prove the Enemy didn't exist. (PROSE: The Book of the War) In the lead-up to the War, the Doctor negotiated with the Celestis; he was subsequently killed on Dronid during the first full-on battle in the War. (PROSE: Alien Bodies)
The ruling Houses promised pardons, political power, and new regeneration cycles to renegades in an attempt to bring them back to the Homeworld. (PROSE: The Book of the War) Some were reintegrated into society; Holsred's biology tutor and Allopta's combat teacher were barely-reformed renegades. (PROSE: The Taking of Planet 5) Others were betrayed, overpowered, lobotomised by military psychosurgeons and fitted with neural links to babels for the Lethean Campaign. (PROSE: The Book of the War)
Near the start of the Last Great Time War, the Time Lords resurrected the Master (TV: The Sound of Drums) in a fashion which injured the Doctor's TARDIS, (PROSE: Doctor Who and the Time War) knowing he would be "the perfect warrior for a time war". (TV: The Sound of Drums) They also granted the Master a new regeneration cycle. (TV: Utopia, The Doctor Falls) Though he was initially reluctant to fight, the Sisterhood of Karn convinced the Eighth Doctor to take part in the Great Time War on the Time Lords' side, prompting his regeneration into a War Doctor (TV: The Night of the Doctor) who went on to have authority over Gallifreyan soldiers in conflicts such as the Battle of Skull Moon. (TV: Hell Bent)
Gallifrey's wisdom in relying on the Doctor in either War was called into question by the Eighth Doctor destroying Gallifrey seeking to end the War in Heaven in one account, (PROSE: The Ancestor Cell) and in others, this same Doctor, (PROSE: Doctor Who and the Time War) or his next self (TV: The Day of the Doctor) destroying Gallifrey to put an end to the Time War between Time Lords and Daleks in others, wiping out the Time Lords in the process. (COMIC: Sky Jacks) The Doctor regretted this act, claiming he had had "no choice"; (TV: Dalek) the Moment later gave the Doctor the opportunity to rewrite that fateful day, changing events so that Gallifrey had only appeared to be gone, but actually been banished into a pocket universe, a trick effected with the reluctant accord of the Eleventh General but without the knowledge or approval of the High Council, (TV: The Day of the Doctor) whose own plans to avert the End had already failed due to the Doctor and the Master. (TV: The End of Time)
After the Wars
After the War in Heaven
In the post-War universe of the War in Heaven, the four surviving Time Lords (PROSE: The Gallifrey Chronicles) who ruled Time as the "Imperial Family" (PROSE: Father Time) included the Emperor, who was a future version of the Eighth Doctor who had destroyed Gallifrey and survived, (PROSE: The Gallifrey Chronicles) and a bearded man wearing a rosette who had once "fought the Doctor across Time and Space", (PROSE: The Adventuress of Henrietta Street) as well as a man with a bent nose and a beautiful young woman (PROSE: The Tomorrow Windows) who matched the descriptions of two more Renegades known to have survived the War one way or another: Iris Wildthyme in her "Jane Fonda" incarnation, (PROSE: Mad Dogs and Englishmen) and Romana IV. (PROSE: Tomb of Valdemar)
Post Time War
In accounts dealing with the Last Great Time War, the Doctor was frequently named as the "Last of the Time Lords", a title he claimed himself; (TV: Gridlock) however, he "was not alone", as the War Master had escaped from the Time War by turning himself into a human using a Chameleon Arch, thus sparing him from the extinction of the Time Lords. (TV: Utopia) The Monk also remained active in the post-Time War N-Space, even before (AUDIO: Divorced, Beheaded, Regenerated) Gallifrey's not-so-triumphant return to the universe. (TV: Hell Bent)
While banished in their pocket universe, the conventional Time Lords granted a new regeneration cycle to the dying Eleventh Doctor (TV: The Time of the Doctor) and also cured the Saxon Master (sent back to the banished Gallifrey by the Doctor after his post-Time War escapades) of his "little condition" before exiling him again, (TV: The Doctor Falls) with him, soon to be her, soon "finding her way back" to the universe. (TV: Dark Water)