[3] Jökull turned professional with Reading on his 17th birthday in August 2018,[4] and spent the first half of the 2018–19 season on loan at Hungerford Town.
[7] Jökull signed for Exeter City on 27 October 2020 on an emergency 7 day loan following injuries to first-team goalkeepers Lewis Ward and Jonny Maxted.
[14] He made his final appearance for Exeter in their FA Cup second-round victory over Gillingham,[9] after which Maxted recovered from his injury and returned to the squad for their next game.
[18][19] On 23 July 2021, Jökull signed a new three-year contract with Reading, before returning to Morecambe on a season-long loan deal.
[25] On 10 August 2023, Jökull extended his contract with Reading until the summer of 2025, and signed for fellow League One club Carlisle United on a season-long loan.
[32] In January 2022, Jökull was called up to the Iceland national team for the first time for matches against Uganda and South Korea in Turkey.