Arngeir is one of the five members of the Greybeards in The Elder Scrolls V: Skyrim. He is the only member who can speak directly to the Dragonborn. Like all the other members, he resides in High Hrothger atop the Throat of the World.
Arngeir acts as the main mentor of the Dragonborn while training him/her. He give them a total of three task to help them master the Thu'um: Concentrating the Unrelenting Force shout by causing projected targets to stagger, using the Whirlwind Sprint shout to bypass a gate quickly, and finally retrieve the horn Jurgen Windcaller from his tomb north of Morthal, although the latter tests initially ends in failure as the horn is seemingly stolen by a mysterious individual (later revealed to be Delphine). They track down the horn and return it to Arngeir, who tells them they have finally mastered the Way of the Voice, they can also return the horn back to the tomb to acquire a dragon soul.
When the time comes, he will have the Dragonborn travel to the peak of the Throat of the World to confront their leader Paarthurnax. He will grant the Dragonborn the Clear Skies shout, which is necessary to reach the top of the mountain.
After the Blades learn that Paarthurnax is alive and once assisted Alduin, they will order the Dragonborn to kill him. If the Dragonborn chooses to kill him, Arngeir will banish the Dragonborn from High Hrothgar, branding them as an enemy and a traitor.