In September 2018, Sylvía Rún joined 1. deild kvenna club Þór Akureyri.
[5] On 5 January 2019, Sylvía posted a quadruple-double with 11 points, 13 rebounds, 10 assists and 10 steals in a victory against Njarðvík.
[2] She averaged 10.3 points and 6.6 rebounds in 22 games for Valur before the season was canceled due to the coronavirus pandemic in Iceland.
[8] In 2016, she was named to the Tournament All-First team during the 2016 FIBA U18 Women's European Championship Division B after leading Iceland to a 4th place finish.
[10] Sylvía's parents, Hálfdán Markússon and Sóley Indriðadóttir, both played basketball for Haukar.