Hlavaj, 22 (5/29/2001), posted a 3.10 goals-against average (GAA) and a .902 save percentage (SV%) in 28 games with HC Škoda Plzeň of the Czech Extraliga this season. The 6-foot-4, 193-pound native of Martin, Slovakia, spent two seasons with HC Slovan Bratislava (2021-23) of the Slovakia League and recorded a 2.47 GAA, a .912 SV% and one shutout in 27 games.
Hlavaj posted a 2.22 GAA and a .932 SV% in three games for Slovakia at the 2023 IIHF World Championship. He also played for Slovakia in three Under-20 IIHF World Junior Championships (2019, 2020, 2021), posting a 4.41 GAA and a .871 SV% in 11 games and played in two Under-18 IIHF World Junior Championships (2018, 2019) where he posted a 4.30 GAA and a .892 SV% in five games.
He played two seasons with the Sherbrooke Phoenix (2019-21) of the Quebec Major Junior Hockey League (QMJHL) and with a 3.84 GAA, a .905 SV% and four shutouts in 59 games. He led the QMJHL in GAA (2.25) during the 2019-20 season and was named the QMJHL Defensive Rookie of the Year, named to the QMJHL All-Rookie Team and to the QMJHL Second All-Star Team.