Four surviving elementals

Following the destruction of Gallifrey and the end of the War, only four Time Lords remained in the universe: the four surviving elementals. (PROSE: The Adventuress of Henrietta Street, Trading Futures) There was in fact a fifth Time Lord to survive the War, Marnal, who remained stuck on Earth as an amnesiac, unaware of his true nature. (PROSE: The Gallifrey Chronicles)

The Onihr claimed to have learned the identities of all four surviving elementals. (PROSE: Trading Futures)

A great number of sources agree that the Eighth Doctor was one of the Time Lords to survive the War. (PROSE: The Adventuress of Henrietta Street et al) Due in large part to the fact that the Matrix was downloaded into his brain, (PROSE: The Gallifrey Chronicles) the Eighth Doctor had very few memories of his life before the end of the War. He and his damaged TARDIS were deposited on Earth in the late 19th century by Compassion. (PROSE: The Ancestor Cell) After living on the planet for over a century, the Doctor regained use of his TARDIS (PROSE: Escape Velocity) and travelled through time and space with Fitz Kreiner, Anji Kapoor, (PROSE: Earthworld et al) and later Trix MacMillan. (PROSE: Timeless et al)

The Man with the Rosette was another one of the four elementals. He believed that since there were only four of his people remaining he had to maintain "certain standards". While once a bitter enemy of the Doctor, the Man with the Rosette remained amicable with the Doctor in the post-War universe. (PROSE: The Adventuress of Henrietta Street)

Iris Wildthyme encountered the Eighth Doctor at least twice in the post-War universe; once in her Jane Fonda incarnation (PROSE: Father Time) and once in her Brenda Soobie incarnation. After his encounter with Brenda, the Doctor proclaimed, "But this means... I am not alone!" To which Fitz somewhat jokingly replied, "There is... another." (PROSE: Mad Dogs and Englishmen) However, the Fonda Iris, (PROSE: The Blue Angel, Interference - Book Two) the Brenda Soobie Iris, (PROSE: The Blue Angel) and even some of the later Irises (PROSE: Library Pictures, A Hundred Words from a Civil War, Michael Drake) had some involvement with the War, indicating that Iris' status in the post-War universe was not definite. Some sources indicate that Iris was not a Time Lord, meaning that she wouldn't even qualify to be one of the four surviving elementals. (PROSE: The Blue Angel, AUDIO: The Elixir of Doom et al) Iris was once hunted down by Herr Drosselmeyr because she was one of the last of her kind. (PROSE: Another Clockwork Iris)

Romana III lived on for many centuries after her final encounter with the Doctor. As an ancient woman, she parked her TARDIS in Janua Foris and told some of its natives the story of her encounter with Valdemar. After telling the story, Romana regenerated into a young, beautiful body with dark eyes and clear ebony skin. (PROSE: Tomb of Valdemar)

Near the end of the universe, the Emperor - the greatest of the elementals - ruled the universe from the Needle, (COMIC: Miranda) which was itself another remnant of the Time Lords: Savar's TARDIS. (PROSE: The Infinity Doctors) The Emperor was the last of his kind, having outlived all of the other Time Lords. Shortly after the birth of his daughter, Miranda, the Emperor was assassinated. For her protection, Miranda was sent back in time to an earlier period of history, where she was adopted by the Eighth Doctor. As she grew up, Miranda exhibited many Time Lord attributes. Miranda eventually returned to her father's era to become the new ruler of the universe. (PROSE: Father Time) She later died during the Eighth Doctor's encounter with the Council of Eight. (PROSE: Sometime Never...)

For at least the Doctor, living in a universe without Gallifrey had its consequences. The second heart of a Time Lord provided a link between them and their homeplanet, but with said homeplanet no longer existing the Doctor's second heart became a poison, pushing him to the brink of death. The Doctor was cured of this malady when Sabbath Dei removed the Doctor's second heart and planted it within himself. (PROSE: The Adventuress of Henrietta Street) The Doctor was able to adapt to having only one heart. (PROSE: Hope)