Career
Breiðablik
Elfar signar 2-year contract with Breiðablik on 31 July 2013. AEK Athens
In 2011, Elfar was signed by Greek giants AEK Athens. He made his debut against Lokomotiv Moscow in the Europa League on 30 October 2011.
His second appearance made against R.S.C. Anderlecht in the Europa League on 1 December 2011, but he never had an opportunity in a Superleague Greece match.
Stabæk
On 23 July 2012 Elfar signed a short term contract with Stabæk for a free transfer until the end of the year. Randers Football Club
On the 31 January 2013 Elfar signed a new short term contract, this time with Randers Football Club from Denmark for the spring season of 2013.
He became a free agent on 1 July 2013. Elfar was part of the Icelandic U21 team in the EURO 2011 in Denmark.
On 10 August 2011, Elfar made his senior debut for Iceland against Hungary.