Sverre started his career with KA at the age of 16 and helped the team win the Icelandic Cup in 1995 and the Icelandic championship in 1997.[3] He won the national championship again in 2006 with Fram.[4]
In 2017, the club was relegated from the Úrvalsdeild.[6] and shortly after, KA decided to break off from the cooperation and fielded their own team starting from 2017 to 2018. Þór continued to run its men's team under the Akureyri name[7] and in 2018, the team finished first in 1. deild karla and was promoted back to the Úrvalsdeild along with KA, which finished second.[8]
On 28 December 2018, Akureyri fired Sverre from his position as head coach.[9]
In 2019, Sverre was hired as an assistant coach to KA. On 6 April 2019 he appeared in KA's last game of the season at the age of 42, stating that it was the final game of his playing career.[10]