Alexandra was initially a service representative for Síminn, Iceland's largest telecommunications company. She joined the Pirate Party in 2014 and campaigned for them in the 2017 parliamentary election. She was appointed to the third position on the party's electoral list in the 2018 Reykjavík City Council elections and became the first deputy councillor for the party at the end of the elections. She was a deputy councillor until May 2021, when she became a councillor and President of the Council. Alexandra is the first transgender person to hold political office in Iceland.
