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, a girl from parallel universe where the Doctor's adventures were recorded as fiction, 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) which he also used when he met a future Sixth Doctor. (AUDIO: The Wrong Doctors) Both Tegan Jovanka and Clara Oswald once used the term "version". (TV: The Five Doctors, COMIC: Time Trick)

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. Rassilon was unsure how many regenerations the Doctor had been granted (TV: Hell Bent) as were and. (TV: The Doctor Falls) The Twelfth Doctor conjectured he might be able to regenerate infinitely. (TV: Kill the Moon

The Timeless Child, as the apparent source of regeneration, appeared to have been free from this regeneration limit, able to cycle between incarnations indefinitely when experimented on by the First Tecteun, with explaining the limit of twelve regenerations having been implemented by the Second Tecteun upon gene-splicing the power to create the Time Lord race. (TV: The Timeless Children) The Thirteenth Doctor asked a later incarnation of Tecteun if "dozens", "hundreds", or even "thousands" of lives were being hidden from her. (TV: Survivors of the Flux) However, another account claimed that Tecteun discovered the ability to regenerate with an inherent thirteen-incarnation limit. (PROSE: The Secret of the Timeless Child)

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. In the presence of matrix projections of his past incarnations, including the War Doctor, the Eleventh Doctor still referred to the Tenth Doctor as his "tenth incarnation". (COMIC: Dead Man's Hand) The so-called Tenth Doctor also once regenerated and kept his face, resulting in a distinct meta-crisis incarnation. Due to his war and meta-crisis incarnations, the Eleventh Doctor had expended all of 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. The Thirteenth Doctor acknowledged upon regenerating that she might be referred to as "the Thirteenth Doctor", even if the title was not entirely accurate. (COMIC: The Many Lives of Doctor Who)

Beyond this, 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, Survivors of the Flux)

Having expended his original twelve regenerations, the Master sought other means to extend his life, by either gaining more regenerations (TV: The Deadly Assassin, The Five Doctors, Doctor Who) or possessing other bodies. (TV: The Keeper of Traken, Doctor Who et al) 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)

The General 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)

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