Ólafur played for IA Akranes and KR Reykjavík before joining Scottish side Hibernian from Keflavik in July 1997 for a fee of £200,000. He played 70 times for Hibs before joining Brentford on a free transfer in May 2000. He went on to play 73 league games for Brentford, at one point having to pay for his own goalkeeping coach. He had a trial with Stockport County in July 2002 and was offered a two-year contract, but chose to remain with Brentford. He was also linked with a move to Ipswich Town, but in November 2002 was forced to retire due to a shoulder injury. He returned to Iceland and resumed his playing career with Grindavik. On his return to the United Kingdom in August 2004, he had a trial with Grimsby Town, before joining Conference South side Margate, moving to Torquay United the following month, as a replacement for the departing Arjan van Heusden. He was one of seven goalkeepers used that season and played 15 league games for Torquay before disappearing in January 2005 when, according to then Torquay chairman Mike Bateson, doping testers arrived at Plainmoor for routine testing and Gottskálksson was chosen to give a sample. On viewing the list of banned substances he fled Torquay, leaving his girlfriend behind without an explanation, and went missing for ten days. In June 2005, the Football Association announced that an independent disciplinary commission had banned Gottskálksson from football indefinitely for failing to take that drugs test.
Ólafur played basketball for seven season in the Icelandic Úrvalsdeild karla, averaging 5.5 points per game for his career. He won the Icelandic Basketball Cup in 1994. He played 4 games for the junior national basketball teams.
Honours
Keflavík
Icelandic Basketball Cup: 1994
Personal life
Gottskálksson was the son of goalkeeper Gottskalk Gottskálksson and the brother of goalkeeper Elvar Gottskálksson.
Legal history
In March 2010 Ólafur was sentenced to a ten months prison term in Iceland for housebreaking, robbery and violent attack. In October 2011 he was sentenced to additional four months in prison for similar charges, including serious violence. On 25 July 2016, he was arrested after a police chase for driving under influences with his five-year-old son in the backseat. He checked into rehab on 4 August but was rushed to the National University Hospital of Iceland two days later due to internal bleeding and broken ribs, injuries he claimed he sustained when the police arrested him.