Hjulmand has also represented Denmark at various youth levels, before making his senior international debut in September 2023, and he was selected for UEFA Euro 2024.

Born in Kastrup, Denmark, Hjulmand progressed through the academy at Copenhagen, he moved to Austria on 13 May 2018 to join Admira Wacker's U-19 squad, signing a contract until June 2022.

[4] Six days later, he also made his debut in the UEFA Europa League, starting in the 3–0 loss to CSKA Sofia, being replaced at half-time by Daniel Toth.

Having started the 2020–21 season with Admira, on 16 January 2021, Hjulmand signed a four-year contract with Italian club Lecce for a fee of €170,000, in the second-tier Serie B at the time.

Under manager Marco Baroni, Hjulmand was entrusted an important role in the team's midfield, with his dynamism, vision, personality, technical and temperamental qualities, placing him among the top players in Serie A for average kilometres covered per match (over 10) and also led the league for the most balls recovered.

[13][14] Five days later, Hjulmand made his debut for Sporting, coming off the bench to replace Marcus Edwards on the 75th minute of a 2–1 league victory away at Casa Pia.

[23] In his first match as club captain, on 3 August, Sporting lost 4–3 to rivals Porto in the 2024 Supertaça Cândido de Oliveira, despite leading the game by three goals.