Most NPC factions in the game are open to all, and can be joined simply by adjusting a character's reputation to the appropriate stance and mounting the proper ID. There are however a few exceptions to this - NPC factions that were usually introduced at the request of a popular player faction, and are since regulated by the recruitment of that faction.
These factions are:
Note that it is impossible to achieve the reputations of the above factions on the Discovery RP 24/7 server without administrator intervention (except Colonial Remnant). Thus, the only way to become part of one of them is to apply for the official faction.