Byskov is a youth product of Herning Fremad and
Ikast, before joining
Midtjylland at the age of 13. On 24 February 2020, he signed his first professional contract with Midtjylland. He worked his way up the latter's youth systems before being promoted to their reserves in 2022. He made his professional and senior debut with Midtjylland as a late substitute in a 5–1
UEFA Europa League win over
Lazio on 15 September 2022. On 28 July 2023, Byskov joined
Liga Portugal 2 club
Mafra on a season-long loan deal. On 3 January 2024 Midtjylland confirmed that the club had recalled Byskov. ==International career==