Incarnation

The term incarnation or regenerative state (AUDIO: Minuet in Hell) was sometimes applied to the bodies/selves/lives of a Time Lord. While it was sometimes used interchangeably with "regeneration", (TV: The Keeper of Traken, Extremis) incarnations were actually the result of this process, with Time Lords regenerating from one incarnation to another.

Use of the term
Looking back on their previous lives, the Doctor occasionally used the word incarnation. (TV: The Twin Dilemma, AUDIO: The Light at the End, The Chimes of Midnight, Dead London, Scaredy Cat) He also used it in reference to the Master, (TV: Doctor Who) and others used it to talk about the Doctor's regenerations, as well. (TV: The Ultimate Foe)

The Eleventh Doctor thought he had never used the word incarnation in that capacity but was proven wrong by Ally, from an alternate dimension, who played a clip from Doctor Who of the Sixth Doctor discussing his "last incarnation" in The Twin Dilemma. He conceded but claimed that the word was hardly ever used. (COMIC: The Girl Who Loved Doctor Who)

With the term being sometimes interchanged with the term regeneration, a Time Lord stating they were in their tenth regeneration would be synonymous in saying they were in their eleventh incarnation. (TV: Hell Bent)

When referring to past incarnations, faces or lives, the Doctor would use "mes", plural of "me". (COMIC: Four Doctors) Time Lords might also use the term "bodies" or "body" when referring, generally, to either their own or other Time Lords' different incarnations. (COMIC: Doorway to Hell) On multiple occasions, the Doctor used the word "persona". (TV: The Twin Dilemma, Time and the Rani) On one occasion, the Sixth Doctor used the word "iteration". (AUDIO: The Light at the End) Tegan Jovanka, a companion of the Fifth Doctor, once used the term "version". (TV: The Five Doctors)

Limit
Barring special circumstances, a Time Lord could only have thirteen incarnations, (TV: The Deadly Assassin) before their symbiotic nuclei started to break down. (AUDIO: Trial of the Valeyard) Some, like the Master (TV: Utopia, AUDIO: Eyes of the Master) and the Doctor, (TV: The Time of the Doctor) have been given new regeneration cycles, bypassing this limit.

The Timeless Child, as the apparent source of regeneration, appeared to be exempt from this regeneration limit, able to cycle between incarnations indefinitely when experimented on by the First Tecteun. (TV: The Timeless Children)

Proto-Time Lords created by the Kovarian Chapter had varying numbers of incarnations. (AUDIO: The Lady in the Lake)

Lifespan
Each incarnation was capable of lasting a few thousand years before wearing out and needing to regenerate, (PROSE: The Novel of the Film) with the Time Lord Handrel specifying that a single incarnation could live for around ten thousand years. (PROSE: The Time Lord's Story)

Retro-regeneration
Retro-regeneration was the process of regenerations being forced in reverse, causing the Time Lord in question to revert to previous incarnations, (COMIC: The Fountains of Forever) though it was not known to be permanent in any cases. (COMIC: Timeslip, The Fountains of Forever, Outrun)

Time Lords by incarnation
Calculating the number of the Doctor's incarnations was complicated, as they rarely referred to themselves by number. Though the Seventh Doctor identified himself as "number seven”, (AUDIO: The Defectors) the Eighth Doctor's immediate successor did not use the title of Doctor until the end of his life, leading to ambiguity from this point forward. Because of his actions during the Time War, his future selves completely denied his existence. The so-called Tenth Doctor also once regenerated and kept his face, resulting in a distinct meta-crisis incarnation. As such, the Eleventh Doctor had apparently expended all his lives before being enabled to regenerate again by the Time Lords. (TV: The Time of the Doctor)

At the beginning of the Thirteenth Doctor's life, the Doctor had regenerated a total of fourteen times. In total, including the Meta-Crisis Doctor, the Doctor had fifteen incarnations. (COMIC: The Many Lives of Doctor Who) A further incarnation was yet to come. (TV: The Day of the Doctor, COMIC: The Then and the Now) Some accounts suggested that the Doctor had more incarnations from before they became the First Doctor, as well, adding to the count. (TV: The Brain of Morbius, The Timeless Children)

Having expended his original twelve regenerations, the Master sought other means to extend his life. (TV: The Deadly Assassin, Doctor Who) Ultimately, the Master was able to regenerate again after he was resurrected by the Time Lords (TV: Utopia, The Sound of Drums) as part of a complex deal made with one of his future selves during the Time War. (AUDIO: Day of the Master) In her Spacebook profile, identified herself as the nineteenth incarnation of the Master. (PROSE: Girl Power!) It was in this incarnation that she was apparently killed by her predecessor, denying her the opportunity to regenerate. (TV: The Doctor Falls) However, she managed to survive the attack and changed into her next incarnation by creating an Elysian field. (AUDIO: The Lumiat)

Drax was known to have had the standard thirteen incarnations. (AUDIO: The Trouble with Drax)

In his thirteenth and final incarnation, Azmael deliberately regenerated past his limit, killing him and Mestor, who had been attempting to possess Azmael's body after his own was destroyed. (TV: The Twin Dilemma)

As her alias suggested, the Twelve was the twelfth incarnation of a Renegade Time Lord who suffered from regenerative dissonance. (AUDIO: Planet of the Ogrons) Other than her, the Time Lord who lasted the longest with this condition shot out both his hearts with a staser in his eighth incarnation. (AUDIO: World of Damnation)

Kenossium was known to have had twelve incarnations. (TV: Hell Bent)

Contact between incarnations
Contact between separate incarnations of the same Time Lord constituted a violation of the First Law of Time. (TV: The Three Doctors)

The Master
When the Master offered to assist the Cult of the Heretic in their plans to remake the universe, they agreed to the offer only if he would kill one of his past selves to prove his loyalty to their cause, as the Anomaly Cage would protect the Master from the resulting paradox. As a result, the Master attempted to ambush his past self during his assault on Tersurus (allegedly planning to just leave his other self in a near-death state that he remembered being in at that time of his life anyway), but the Cult deliberately sabotaged this attack so that they could create a more potent paradox by transferring the younger Master into the body of his future self and then kill the older Master in his past incarnation. The two Masters were able to escape the Cult with their immediate memories scrambled, but their travels in the wrong bodies nearly destroyed the universe due to the paradox, with whole segments of history being erased - including meetings with the Fifth and Sixth Doctor s - until the Seventh Doctor confronted both Masters at once and helped them realise what had happened. The Masters returned to their own bodies and attempted to leave the Doctor to die so that they could hijack the Cult's plan to remake the universe, but the Doctor was able to follow them and restore reality as it was, apart from sending the Masters back to their points of origin with no recollection of their interactions with the Cult. (AUDIO: And You Will Obey Me, Vampire of the Mind, The Two Masters)

, the nineteenth incarnation of the Master, (PROSE: Girl Power!) travelled through her time stream to recruit her, Tremas,  Bruce and , forming a band to compete on Battle of the Bands Beyond the Stars. The group planned to use the popularity of the program to hypnotise the audiences across the galaxy. According to Missy, the five spent "decades" preparing for the performance. (COMIC: The Five Masters) The group went on before the Twelfth Doctor and Clara Oswald due to a shift in the program's schedule, and the five revealed themselves to the pair. (COMIC: The Abominable Showmen) Missy expected the Doctor to attempt to stop the five of them, or to at least esquire on their plans, but the Doctor refused to intervene or question their scheme. After much prying, the Doctor correctly predicted the group's plan, but still refused to intervene as they started their song. As she prepared to hypnotise her audience, her previous incarnations began to fight with her over her device, as each wanted to control the universe without the others. During the fight, viewers began to turn off their sets and the group were soon all disqualified and were thus blown up, although neither Clara nor the Doctor believed that they had truly been killed. (COMIC: The Five Masters)

When the Eleven formed an alliance with the Ravenous, the Master became aware of it in three different incarnations; the Master in Bruce's body met the Eighth Doctor while working with the Gallifreyan scientist Artron to try and gain new life energy in Gallifrey's distant past, the War Master responded to a call for help sent by Liv Chenka from a Time Lord waystation the Master had claimed as a base, and Missy later responded to another call for help from her predecessors and abducted Helen Sinclair to pursue another lead to Artron's current location. Not wanting the Ravenous to destroy the universe, the three Masters collaborated to undo the Eleven's plan to grant all life in the universe the ability to regenerate via the Crucible of Souls while the Doctor helped Artron realise how he could stop the threat posed by the Ravenous. When the Eleven attempted to propose an alliance between himself and the Masters against the Doctor, the Masters shot the Eleven and abandoned him with a vortex manipulator as he began to regenerate. The alliance between the Masters concluded with the revelation that the War Master had been assigned by the Time Lords to retrieve Artron's Matrix print from the Eleven so that it could be used to give Time Lords a new regeneration cycle, only taking a detour to restore a dead version of themselves to life (a future version of the Master in Bruce) with a new cycle of standard regenerations as part of the War Master's deal with the High Council. (AUDIO: Day of the Master)

Missy later inadvertently came into contact with her immediate predecessor aboard a Mondasian colony ship while in the company of the Twelfth Doctor. (TV: World Enough and Time) Though they initially joined forces, Missy ultimately elected to side with the Doctor against the Cybermen, resulting in her being killed without the opportunity to regenerate by her predecessor, though not before she mortally wounded him and thus initiated his regeneration. (TV: The Doctor Falls)

Others
Eleven of Drax's thirteen incarnations teamed up in order to con the Fourth Doctor into stealing a Blinovitch Limitation Effect limiter, which was what allowed them to cooperate on this scheme in the first place. It would appear that the Draxes used this technology to complete various other schemes in their lives, the different Draxes working together to complete complex plans that would have been harder for any individual incarnation to pull off. (AUDIO: The Trouble with Drax)

Behind the scenes
In the cinema introduction to The Day of the Doctor, the Eleventh Doctor claimed that "all 57 Doctors" would appear in the 100th anniversary special of Doctor Who in 2063.

Inkarnace