[7][8] After years of development at the academy, Hjörtur made his professional debut as Jong PSV player in the Eerste Divisie on 18 August 2013 against FC Oss in a 4–0 home win.

[10] In the 2014–15 season, Hjörtur continued to remain in the Jong PSV starting eleven despite suffering setback of injuries, which restricted him to 16 appearances.

[11][12] During the season, Hjörtur was called up to the senior team ahead of the match against NAC Breda, but did not play, as PSV went on to win 2–0 on 3 February 2015.

[24][25][26] With the Danish side, he also took part in UEFA Europa League qualifiers, never making it to the group stage as they were knocked out to Panathinaikos (2016), Hajduk Split (2017), Genk (2018), Braga (2019).

In the 2019–20 season, Hjörtur was utilised as the right-side centre-back in the 3–5–2 formation of head coach Niels Frederiksen, alongside team captain Andreas Maxsø and Anthony Jung.

[34] Hjörtur scored his first goal for Pisa on 29 May 2022 in the play-off finals for promotion to the Serie A against Monza off a cross from Pietro Beruatto.

[35] Two goals in extra time by Monza won them the encounter 4–3 (6–4 on aggregate), to earn promotion to the 2022–23 Serie A, with Hjörtur and Pisa missing out.

[47] It wasn't until on 31 January 2016 when he made his senior team debut, coming on as a substitute in the second half, in a 3–2 loss against United States.

[49] However, Hjörtur did not make any appearance for Iceland throughout the UEFA Euro 2016, as they reached the quarter-final and lost to France.