Peterka was selected by the Buffalo Sabres in the second round (No. 34) of the 2020 NHL Draft. He played one season for Rochester of the American Hockey League, led the team with 68 points (28 goals, 40 assists) in 70 games and scored his first NHL goal for the Sabres on opening night of the 2022-23 season, a 4-1 win against the Ottawa Senators on Oct. 13. Five days later, Peterka became one of four Buffalo rookies to open a season with a point in each of his first three games (Tyler Ennis, 2010; Calle Johansson, 1987; Victor Olofsson, 2019). He joined Olofsson on Oct. 20 as the only Sabres first-year players with a point in each of his first four games.

Peterka played three full seasons for the Sabres before he was traded to the Utah Mammoth on June 25, 2025. Over the previous two, his 55 goals and 63 assists each ranked third on Buffalo, fourth in the NHL and eighth in points among all players aged 23 or younger. He then signed a five-year, $38.5 million contract ($7.7 million average annual value) with Utah in lieu of becoming a restricted free agent.

A native of Munich, Germany, Peterka was named to Team Germany's roster for the Olympic Winter Games Milano Cortina 2026. He had 20 points (nine goals, 11 assists) in 30 games for EHC Munchen of DEL, the top professional league in Germany, in 2020-21 and had one goal in six games at the 2021 IIHF World Championship. He was an alternate captain for his home country at the 2021 IIHF World Junior Championship, where he had 10 points (four goals, six assists) in five games.