She was named the Icelandic Women's Basketball Player of the Year twice, in 2017[1] and 2018, and was a four time selection to the Úrvalsdeild Domestic All-First Team.

After coming up the junior ranks of Snæfell, Hildur played her first game for the senior team during the 2009-10 Úrvalsdeild kvenna season.

[6] In August, she exercised an escape clause in her contract with Breiðablik and signed with Club Baloncesto Leganés of the Spanish Liga Femenina 2.

[12][13] On 13 May 2020, Hildur signed with Valur[14] after KR failed to give her a contract offer or any answers on the future of the team in the aftermath of the coronavirus pandemic in Iceland.

[22] On 24 January 2024, Hildur Björg announced her retirement from playing basketball[23] due to repetitive head injuries, including two during the season.