Elrhûn is the son of Annael, a Sinda elf who will later foster Tuor in Dor-lomin.
Annael and his family are introduced in Season 4, and then Annael is captured and becomes a prisoner in Angband during the Dagor Aglareb. While his father is away, Elrhûn enters Fingon's service. When Fingon's herald is killed while fighting Glaurung, Elrhûn becomes Fingon's herald in Season 5.
When Annael escapes from Angband, he joins Fingolfin's court. Which makes him a very strategically placed mole. In Season 6, his unwitting treachery will be revealed during the fall of Minas Tirith at Tol Sirion. At that time, Annael will choose exile, and Elrhûn will remain with Fingon. Presumably, Elrhûn will die in the Nirnaeth, when Gothmog's troll guard targets Fingon.