There are three factions added by the Tribunal expansion, none of which are joinable.
This guild of assassins split from the Morag Tong years ago, and have been employed by various wealthy individuals, notably King Hlaalu Helseth, to snuff out bothersome individuals within the province. Assassins from this guild will be the first people you meet when you start the Tribunal quest line, as they will attempt to murder you in your sleep. There is only one named member of the faction in the game: Dandras Vules. While there were various Dark Brotherhood members encountered in Morrowind without the expansion, the official faction did not exist, and these NPCs were technically not part of any faction.
These are the personal bodyguards of Almalexia, and can be found at her side within the Temple. They are a subset of the High Ordinators, themselves members of the Tribunal Temple and affiliated with House Indoril. Their sole purpose is to serve and protect their mistress, the goddess Almalexia.