Born in 1993, Hjörvar earned his FIDE master title in 2011, followed by his international master title in 2012 and grandmaster title in 2013. He first competed for Iceland at the 39th Chess Olympiad, scoring 4/7. He has since represented his nation at the 40th Chess Olympiad, scoring 6½/10; the 41st Chess Olympiad, scoring 7/10; and the 42nd Chess Olympiad, scoring 7/10.