Sisterhood of Karn

The Sisterhood of Karn was a female society dedicated to protecting the Sacred Flame, which produced the Elixir of Life. (DW: The Brain of Morbius)

The Sisterhood was a remnant of the Pythia's power. (NA: Cat's Cradle: Time's Crucible)

The Great Mother of the Sisterhood and her High Priestess Cassandra, from the House of Jade Dreamers, plotted to destroy Rassilon's Foundry along with Lord Provost Tepesh and Lady Ouida from 'The Committee of Three'. Tepesh and Ouida, who were also Vampires, murdered Cassandra before all were killed by the automated sterilisation of the Foundry. (BFA: Zagreus)

The Sisterhood entered into the Pact of Rassilon for protection under Gallifrey. They also fought against Morbius when he attempted to invade Karn. (PDA: Warmonger)

When the Sacred Flame appeared to be dying, the Sisterhood suspected the Fourth Doctor of trying to steal the remaining Elixir, but later helped him defeat Morbius. In reality, the only thing wrong with the Flame was that centuries of ash and soot were finally beginning to clog the underground fissure that fed the flame natural gas. The Doctor easily solved the problem by dropping a simple firecracker down the shaft. (DW: The Brain of Morbius)

After Romana became President of Gallifrey, she opened diplomatic relations with the Sisterhood. (NA: Lungbarrow)

The Sisterhood were capable of teleportation using the Sacred Flame. They later tried to prevent Morbius' resurrection; failing to do this they saved the Eighth Doctor after he threw himself and Morbius into the core of Karn. (BFA: Sisters of the Flame / The Vengeance of Morbius)

Behind the scenes
They appear to be based on the Bene Gesserit sisterhood in the book series Dune by Frank Herbert. The term "reverend mother" is used by the Bene Gesserit, and "elixir of life" is similar to a Bene Gesserit term.