Early career

Nagy began skating under coaches Oleg Efimov and Natalia Efimova, a former Soviet pairs skater and ice dancer, respectively, in Wake Forest, North Carolina.^[2] During this time, he also trained as a gymnast at Apex Gymnastics under coaches Todd McLoughlin and Jeremy Waters. He trained primarily in singles skating, representing first the United States, and then Hungary internationally after his family moved back to Budapest. At the suggestion of his coaches, Nagy briefly tried pairs with Krystal Edwards during the 2011–12 season, but the team split due him being "not ready" and his family returning to Hungary.^[2]

Nagy briefly quit skating in 2017, before deciding to return and switch to pairs full-time.^[2] He tried out with Kate Finster in the fall of 2017, around Thanksgiving, and they officially teamed up in early 2018.^[2] The pair relocated from training with her coaches, Jessica Miller and Stephanie Miller, in Northern Kentucky to work full-time with Dalilah Sappenfield and Larry Ibarra in Colorado Springs.^[2][1]

2018–2019 season

In their first season as a team, Finster/Nagy were assigned to 2018 JGP Czech Republic, where they finished ninth. They then won silver at Midwestern Sectionals. At the 2019 U.S. Championships, Finster/Nagy won the junior silver medal behind Lockley/Prochnow. As a result, they were named to the 2019 World Junior Championships team. At Junior Worlds, they were tenth after the short program and thirteenth in the free skating, to finish eleventh overall. Nagy called the experience "humbling" and motivation for the next season.^[2]

2019–2020 season

Finster/Nagy opened the season with a sixth-place finish at 2019 JGP United States. They then won their first international medal at 2019 JGP Poland, earning the silver medal, behind Panfilova/Rylov of Russia and ahead of Germany's Hocke/Kunkel.^[4] Their results qualified them as first alternates to the 2019–20 Junior Grand Prix Final.

Finster/Nagy won the inaugural U.S. Pairs Final to qualify to the 2020 U.S. Championships. They won their first junior pairs title at the 2020 U.S. Championships, ahead of Smirnova/Siianytsia and Deardorff/Johnson. Their result earned them a berth on the 2020 World Junior Championships team.^[5] They finished sixth.^[6]

2020–2021 season

Finster/Nagy placed ninth at the ISP Points Challenge.

In December, Nagy announced that the pair had split.^[7]

2021–2022 season

Nagy formed a new partnership with Russian skater Maria Pavlova to represent his native Hungary. Making their debut at the Budapest Trophy, where they were seventh, they then competed twice on the Challenger series, finishing fifth at the 2021 Denis Ten Memorial Challenge and thirteenth at the 2021 CS Golden Spin of Zagreb.^[8]

After winning the silver medal at the 2022 Four National Championshipss and the Hungarian Championships, Pavlova/Nagy made their debut at the European Championships, finishing eleventh.^[8]

The pair parted ways following the season. Nagy would later explain that "I fell out of love with the sport, so I stepped away for a little bit. I had surgery again–my other shoulder. While I was recovering from that one, that was when I reached out to U.S. Figure Skating."^[9]

2023–2024 season

In April of 2023, Nagy tried out with Chelsea Liu.^[10] They announced their partnership in May.^[11]

Liu/Nagy made their domestic debut by winning the Glacier Falls Summer Classic, before being sent to make their international debut on the Challenger debut at the 2023 CS Autumn Classic International. They attracted notice for their innovative climactic lift in the free skate, but finished fourth.^[9] They were subsequently invited to make their Grand Prix debut at the 2023 Skate America, finishing third in the short program with a new personal best score (61.23).^[12] They were third in the free skate as well, despite Liu making two Salchow errors, winning the bronze medal. Liu said that "winning a medal on the Grand Prix is great, but what feels even better is that we put out a great program."^[13] Liu/Nagy went on to place sixth at the 2023 NHK Trophy.^[14]

In advance of the 2024 U.S. Championships, Liu/Nagy were preemptively assigned to the American team for the 2024 Four Continents Championships in Shanghai, which were to occur a week after the national championship.^[15] At the national championships, they finished sixth in the short program. In the free skate they came third in the segment, moving up to fourth overall in the process, despite struggles on their jump and throw elements. Nagy said they were "a little bit frustrated that we were not able to show off our throws the way they've been in training."^[16] At the Four Continents Championships the following weekend, Liu/Nagy came third in the short program, winning a bronze small medal, despite Liu stumbling out of her jump. Liu said that they had "been working so hard on our throws and they've been so good since the New Year. I'm super happy that we were able to show that."^[17] They had a difficult free skate, and dropped to seventh.^[18]

On March 26, Liu announced she had ended her partnership with Nagy to prioritize her mental health.^[19]

With Liu

With Pavlova

With Finster

With Liu for the United States

With Pavlova for Hungary

With Finster for the United States

Men's singles for Hungary

With Liu

With Pavlova

With Finster