[3] In 2009, at the age of sixteen, he joined the Hamburger SV academy for a trial, before returning the Lyngby where he signed a contract extension the following year.
[4][5] Gytkjær was promoted to the Lyngby first team in the summer of 2012 alongside fellow academy players, among other Uffe Bech who would go on to play for Hannover 96 and Panathinaikos later in his career.
[10] During these two seasons, ending in promotion to the Danish Superliga, Gytkjær scored 20 goals in 45 league appearances, marking a more offensive role for the midfielder.
[13] On 6 July, Gytkjær made his European debut starting in a 0–0 away draw against Northern Irish club Coleraine in the first qualifying round of the 2017–18 Europa League.
[14] After advancing 7–0 on aggregate, Haugesund drew Polish club Lech Poznań in the second round, meaning a matchup between Gytkjær and his brother, Christian.
[23] He suffered a concussion in a league match against FC Fredericia on 28 February 2022, sidelining him for the rest of the season which saw Lyngby win promotion back to the Superliga.