Father Elijah

 was an elder and leader of part of the west-coast Brotherhood of Steel.

Background
He went missing during the NCR takeover of the HELIOS One powerplant and was never found. According to Head Paladin Hardin, his becoming an elder was questionable due to his status as a scribe; normally, the ability to become an elder is reserved for Paladins, though in Elijah's case an exception was made due to his high intelligence. Veronica refers to him as still alive as he contacted her after the HELIOS One disaster.

During the quest Still in the Dark, after talking to some of the members of the Brotherhood of Steel, you find out Elijah became an elder because he was a genius. However, the members say he was a strange man and his battle tactics were poor. They then tell you during the takeover of HELIOS One he held them inside the building too long. He kept saying 'something was almost ready'. This is most likely hinting to the Archimedes II.

In the add-on, Dead Money, it is revealed that Elijah discovered the Sierra Madre whilst searching for weapons to eradicate the NCR. It is hinted at that he is the person who activates the radio signal luring the player to the Sierra Madre, possibly meaning you may get to meet him.

In the "Dead Money" trailer it is possibly Elijah speaking beacause at a point where the courier passes some sort of blue communication orb, you can just about make out a face wearing a brotherhood elder robe, you can see the low shoulders and high collar, plus it make sense to be him considering the notes he left behind.

Appearances
is only mentioned in Fallout: New Vegas.