The Great Vampires were massive humanoids in Gallifreyan legend that lived during the Dark Times.
Biology
The Great Vampires were colossal humanoids with grey skin and wings. Like lesser vampires, Great Vampires needed blood to survive, but their large size dictated they needed considerably more. Great Vampires were extremely powerful and one individual could drain a whole planet dry. They could absorb energy in almost any form and survive numerous minor wounds. The only way to kill one was to stab them through the heart, usually with a steel bolt. More powerful Great Vampires needed to have their heart fully destroyed in order to kill them. (DW: State of Decay)
History
Reign
The Great Vampires suddenly appeared in the universe, causing mass destruction and chaos. (DW: State of Decay) They rampaged through the cosmos during the Dark Times. (DW: The Infinite Quest) Great Vampires created the Vampires on Earth. (EDA: Vampire Science) They may have been the Yssgaroth (FP:The Book of the War).
War with the Time Lords
Eventually Time Lords hunted these creatures down in a long and bloody war, using bowships firing mighty bolts of steel to pierce their hearts. Though the Time Lords won, they took heavy losses. The leader of the Vampires escaped into the smaller universe of E-Space. Over time records of this war were lost and passed into legend. Rassilon wrote data about the vampires that was installed into every Type 40 time vessel. It said that one vampire, the King Vampire, had vanished and it was a Time Lord's solemn duty to lay down his life to kill it. This war was said to have sickened Time Lords of violence forever. (DW: State of Decay)
The King Vampire
The King Vampire fell into E-Space, using his great power to draw the ship Hydrax with him. He turned the people on this ship, three humans, into vampires. They fed and served him for a thousand years until the Time of Arising. As he rose from the ground the Fourth Doctor used a Scout ship from the Hydrax to pierce his heart, killing him. (DW: State of Decay)
An alternate perspective
During the events involving Doctor's infection with Anti-Time, the TARDIS constructed a holographic projection of events from the Gallifreyan Time of Chaos.
In this projection, a group of Gallifreyans investigated Rassilon's work on regeneration, time travel, and other projects. The prime investigator was the head of the Arcalian Chapter Houses, Provost Lord Tepesh. In the projection, Tepesh revealed himself as a Great Vampire in disguise, even saying he was a direct descendant of the King Vampire.
Tepesh claimed the Great Vampires were a peaceful lot, content to drink the blood of non-sentient, genetically bred cattle, until Rassilon showed up and declared the Vampires should not be allowed to exist. The subsequent 500-year war was more one of extermination than titanic conflict. (BFA: Zagreus)
The TARDIS declared this projection to be only partially based on reality. It is unknown how much of this projection accurately reflected real events.