Vladar's 42 saves in a 1-0 win against the Pittsburgh Penguins in Game 6 of the 2026 Eastern Conference First Round were the most by a Philadelphia Flyers goalie in a series-clinching victory, passing the previous high of 41 held by Phil Myre in Game 3 of the 1980 Preliminary Round. The 42 saves were also the fourth-most in a series-clinching shutout win over the past 70 years behind Patrick Roy (63 in Game 4 of the 1996 Stanley Cup Final), Andrei Vasilevskiy (49 in Game 4 of the 2022 second round) and Carey Price (43 in Game 6 of the 2015 first round).

Vladar signed a two-year, $6.7 million contract with the Flyers on July 1, 2025, after four seasons with the Calgary Flames organization. He played for Team Czechia at the Olympic Winter Games Milano Cortina 2026.

The native of Prague, Czechia, was selected by the Boston Bruins in the third round (No. 75) of the 2015 NHL Draft and was traded to the Flames on July 28, 2021. He played five seasons for Boston's American Hockey League affiliate in Providence, where he went 36-26-13 with a 2.33 goals-against average and .917 save percentage. His 1.79 GAA and .936 save percentage in 2019-20 each ranked first in the AHL.

Vladar played minor hockey in Czechia and at the 2015 IIHF World Junior Championship.