Hjálmar came up through the junior ranks of Haukar and started his senior team career during the 2013–14 season.

In August 2020, Hjálmar signed with Liga EBA club Aquimisa Carbajosa[1] where he met fellow Icelander Tómas Þórður Hilmarsson.

[2][3] In February 2021, it was reported that Hjálmar would leave Carbajosa and return to Iceland to join Valur,[4] much to the displeasure of Haukar who threatened legal action as they believed that he was still under contract obligations to not to play for any other team in Iceland except them until after the season.

[9] On 24 September 2023, he won his second straight Icelandic Super Cup after Valur defeated Tindastóll 80–72.

[11] He was a member of the team that won silver at the 2019 Games of the Small States of Europe.