[2][3] Teitur Örn Einarsson made his debut for his boyhood club Selfoss in the 2015/2016 season where he helped his team secure a promotion to Úrvalsdeild.
[4] In the summer of 2018 he moved to the Swedish Handbollsligan to IFK Kristianstad, where he signed a two-year contract.
[5] In October 2021 it was announced he had signed with German SG Flensburg-Handewitt, starting immediately.
[6] Teitur was the top scorer of the 2017 Men's Youth World Handball Championship in Georgia with 66 goals.
[7] On 5 April 2018 he made his debut for the Icelandic national team in a 29–31 loss against Norway in a friendly.