Fábián was born and raised in Szeged, and moved to Budapest in 2021 to train with the Ferencvárosi Torna Club.

[2] At the 2021 European Junior Swimming Championships in Rome, in July 2021, Fábián won a gold medal in the 4×200 metre freestyle relay, and a silver medal in the 400 metre freestyle, with a time of 4:10.16.

[7] In July 2023, she competed at the 2023 World Aquatics Championships in Fukuoka, and won a silver medal in the team relay with a time of 1:10:35.3.

[8] In February 2024, she competed at the 2024 World Aquatics Championships in Doha, and won a bronze medal in the team relay with a time of 1:04:06.8.

[10][11] She competed at the 2024 Summer Olympics in Paris in the 10 km open water marathon and finished in fifth place with a time of 2:04.16.9.