Ægidius began his football journey at the local club Slangerup & Omegn IF in 2008, where he played until 2011 before moving to FC Nordsjælland.[1] In the winter of 2016, Ægidius transferred from Nordsjælland to Lyngby Boldklub.[2]
At Lyngby, Ægidius became part of the club’s academy and over the years featured for all youth national teams. On 11 November 2020, the 18-year-old made his debut for Lyngby’s first team in a Danish Cup match against Slagelse B&I, coming on as a substitute for Frederik Schram in the 73rd minute of the 9–0 victory.[3][4][5]
On 25 January 2021, Ægidius signed a four-year pre-contract with Brøndby IF, which meant he would move from Lyngby to Brøndby on a free transfer in the summer of 2021, when his contract with Lyngby expired.[6] A few days later, on 1 February 2021, the clubs agreed that Ægidius would transfer immediately.[7]
In his first one and a half seasons at Brøndby, Ægidius primarily played for the club’s U-19 team. In pursuit of senior experience, he was loaned out to the Danish 2nd Division club HIK on 18 July 2022 until the end of the season.[8] Ægidius made his debut for HIK on 6 August 2022 against BK Frem.[9] He went on to play two more matches, receiving a red card after an hour in the last game, before being recalled by Brøndby on 29 August 2022 due to injuries in their squad.[10]
After being recalled, Ægidius continued as the third-choice goalkeeper at Brøndby and made only a few appearances for the club’s reserve team that season. Nevertheless, in July 2023, he signed a contract extension with Brøndby until June 2027.[11][12]
In July 2024, still awaiting his debut for Brøndby, Ægidius was loaned out to the Danish 1st Division club Kolding IF for the 2024-25 season.[13] However, he was recalled at the end of 2024, after 11 games for Kolding.[14]
On 3 February 2025, Ægidius returned to Lyngby Boldklub, signing a contract until June 2028.[15][16] On 21 March 2025, Ægidius got his Lyngby- and Danish Superliga debut, when he was in the starting lineup against Viborg FF.[17][18]