Jászapáti made his first international appearance at the 2013 Junior World Championships in Erzurum . Her best placings were 22nd place in the all-around competition and tenth place with the relay. She made her debut in the World Cup at the beginning of the 2014/15 season in Shanghai , finishing 24th over 500m and 20th over 1000m. At the 2015 European Championships in Dordrecht , she won the bronze medal with the relay. Her best results at the 2015 World Championships in Moscow were 20th place over 500 m and fifth place with the relay. In the 2015/16 season he achieved her first podium finishes in the World Cup in Dresden with third place over 1000 m and second place with the relay. At the 2016 European Championships in Sochi , she finished 13th in the all-around competition and fourth in the relay. Her best placement at the 2016 World Championships in Seoul was 18th over 500 m. At the 2016 Winter Youth Olympic Games in Lillehammer , she won the silver medal in the 500 m. In addition, she took fourth place over 1000 m there. In November 2016, she was third with the relay at the World Cup in Calgary . At the junior championships in Innsbruck at the end of January 2017 , she was third in the 1500 m. At the European Championships 2017 in Turin and the World Championships 2017 in Rotterdam , she won the silver medal with the relay. The following year she won the silver medal with the relay at the European Championships in Dresden and won fourth place in the all- around at the Junior Championships in Tomaszów Mazowiecki . Her best placements at the 2018 Winter Olympics in Pyeongchang were sixth place over 1500 m and fourth place with the relay.
In the 2018/19 season, Jászapáti won her first World Cup victory with the mixed relay in Salt Lake City over 500 minutes in Almaty . In addition, she was second with the mixed relay in Dresden and at the end of the season reached fifth place in the World Cup over 500 m. At the 2019 European Championships in Dordrecht , she won the bronze medal with the relay and finished ninth in the all-around competition. In the 2019/20 season she won the mixed relay in Dresden and came eighth overall with three top ten placements over 500 m, including third place in Salt Lake City. At the European Championships 2020 in Debrecen she finished 15th in the all-around competition and fourth in the relay.