Upon moving to North America, Fehérváry began playing with Washington's American Hockey League (AHL) affiliate, the Hershey Bears.

He also spent his sophomore season with the Bears before earning a place in the Capitals lineup in 2021 following the departures of Zdeno Chára and Brenden Dillon.

[4] He then attended the Svišt Hockey School, which his parents founded,[5] and played forward until the age of 11 when his coach transitioned him to defence.

[5] He joined the Malmö Redhawks for their 2014–15 season and quickly climbed their ranks from U16, U18, and U20 before making his Swedish Hockey League debut at the age of 16.

[16] He attended the Capitals' 2018 rookie and main training camps, before he was re-assigned to return on loan to SHL club, HV71, for the duration of the 2018–19 season.

[26] Following another recall in February, Fehérváry replaced Nick Jensen on defense for the Capitals and tallied up his first NHL point, an assist, in a 7–2 loss to the Philadelphia Flyers.

[27] Once the NHL was paused due to the COVID-19 pandemic, Fehérváry returned to his home country and continued to work towards his degree in sales and marketing.

[28] Once the NHL resumed play for the 2020 Stanley Cup playoffs, Fehérváry was invited to participate in the Capital's training camp ahead of the postseason.

[32] Following the conclusion of the 2019–20 season, the Capitals signed three right-handed defensemen in the offseason; Justin Schultz, Trevor van Riemsdyk, and Paul LaDue.

[35] He finished the season with three goals and 14 assists for a career-high 17 points through 24 games, and received the teams' Milton Garland Memorial Award for Bears Best Defender.

[36] After spending the pandemic-shortened 2020–21 season with the Bears, Fehérváry returned to the Capitals lineup in 2021–22 following the departure of Zdeno Chára and Brenden Dillon.

[39] Following the re-assignment of Michal Kempný on 10 October,[40] Fehérváry joined John Carlson on the first defensive pair where he was praised for his confidence in his shut-down roles.

[43] Throughout the second half of the season, Fehérváry continued to improve defensively and ranked second among rookies in hits while also playing an average ice time of 19:42.

He was then invited to represent Slovakia men's national ice hockey team at the 2018 IIHF World Championship where he tallied two assists.

As a result of his defensive skills, Fehérváry was given increased responsibility on the ice which included defending against the other top defencemen in the tournament.

[53] He soon regained the chance to represent Slovakia at the international level during the 2022 IIHF World Championship following Washingtons elimination from the Stanley Cup playoffs.