Alfons started his career with local club Breiðablik in Kópavogur in 2015, playing a single cup game, before going on loan to Þór from Akureyri for the latter half of the season.

[3] He spent three seasons there without ever cementing his place, spending time on loan at IF Sylvia and Landskrona BoIS in Sweden and Breiðablik in Iceland.

[7] He joined English League One (third-tier) club Birmingham City on 12 August 2024 on loan for the season.

[8] He made "a solid, no nonsense debut" the next day as a second-half substitute in Birmingham's 1–0 EFL Cup win away to Charlton Athletic.

[9] Alfons is as of 15 November 2020 the highest capped player of the Icelandic U21 national team with 30 games.