Regeneration cycle

A life cycle refered to the set of regenerations, totaling twelve, which were possessed by a single Time Lord, allowing for thirteen incarnations before death. (TV: The Five Doctors) In certain cases, however, the Time Lords proved able to bestow additional regenerations. (TV: The Sound of Drums, The Time of the Doctor)

The Master

The Master had expended his initial life cycle, but cheated death by possessing the body of the Trakenite Tremas. (TV: The Keeper of Traken) In return for retrieving the Doctor from the Death Zone on Gallifrey, Lord President Borusa offered to bestow upon the Master a new life cycle. Ultimately, the Master did not receive the life cycle from the High Council. (TV: The Five Doctors)

Eventually, however, the Master, having been resurrected by the Time Lords to fight in the Last Great Time War, possessed the ability to regenerate again. (TV: Utopia, The Sound of Drums)

Another Time Lord who lived beyond their initial life cycle was the Doctor. (TV: The Time of the Doctor) Having abanonded their title for the vast majority of their ninth life, (TV: The Day of the Doctor) and distinctly retaining their current form following their eleventh regeneration, the so-called Eleventh Doctor was actually the twelfth incarnation and last of the first thirteen lives of the Doctor. On the verge of dying of old age at the Siege of Trenzalore, the Doctor was granted additional regeneration energy by the Time Lords through a crack in time above the planet, allowing him to resolve the conflict and regenerate for the thirteenth time. (TV: The time of the Doctor)

However, the Twelfth Doctor remained uncertain of the amount of new regenerations he had access to, (TV: Kill the Moon) with even Rassilon not being sure how many were granted to him. (TV: Hell Bent) The Thirteenth Doctor was the second incarnation of the Doctor's second life cycle. (TV: Twice Upon a Time)