[4] After spending the 2011–12 and 2012–13 seasons as an overage player with the Primavera (under-19) team, Hörður was promoted to the first-team squad ahead of the 2013–14 Serie A campaign.

[citation needed] Initially part of Juventus’ first-team training camp, Hörður was soon transferred to Serie B side Spezia Calcio on a co-ownership agreement[5] completed on 5 August 2014 for €1 million.

[7] In June 2014 Juventus bought back the 50% share of the player's contract that they had sold to Spezia one year earlier, for €1 million, and immediately loaned Hörður out to Serie A outfit A.C. Cesena on 23 July 2014.

[9] On 13 July 2016, it was announced that Hörður had signed for Championship side Bristol City for an undisclosed fee, penning a three-year deal.

On 28 March 2017, Hörður scored his first goal for Iceland in a 1–0 friendly international win against the Republic of Ireland at the Aviva Stadium.