In July 2011 Hólmbert transferred to Fram Reykjavík after making his mark as a young player with HK in the Icelandic second tier.
[2] Keflavík-born[3] Hólmbert emerged as a stand out player during the 2013 season and his 10 goals were crucial to help Fram Reykjavík avoid relegation from the Icelandic top league.
[5][6] After trials in the Netherlands with Heracles and in Scotland with Celtic, Hólmbert signed a four-year deal to join the Glasgow giants, for a fee of around £100,000.
[7] Although officially signing for the team on 1 January 2014 for the next transfer window, the player started training with his new club at the beginning of December 2013.
[10][11][12][13][14] Hólmbert joined Danish Superliga club Brøndby on loan in September 2014, after failing to feature in any competitive games for Celtic.