Nemec began playing at the highest level in Slovakian hockey, Tipos Extraliga, starting in the 2019–20 season at the age of 15 with HK Nitra.

[6] Nemec was selected fourth overall by the Cape Breton Eagles in the 2021 Canadian Hockey League (CHL) import draft, but he elected instead to play his draft-eligible season in Slovakia.

[8] Following the 2021–22 Slovak Extraliga season, Nemec was seen as one of the top defensive prospects heading into the 2022 NHL Entry Draft and debated alongside Czech David Jiříček as the defenceman to be taken first.

[13] Nemec made the move to North America for the 2022–23 season, spending the entirety of the campaign with the Devils' American Hockey League (AHL) affiliate, the Utica Comets, and recording 12 goals and 22 assists in 65 games.

[20][21] After participating in the aborted 2022 World Junior Ice Hockey Championships, cancelled as a result of the COVID-19 pandemic, Nemec was named to the Slovak squad for the 2022 Winter Olympics.

[20][2] In his second outing of the year with the senior team at the 2022 IIHF World Championship, Nemec lead all Slovak defencemen in scoring with one goal and five assists in eight games.