Juelsgård is a product of Midtjylland's football academy, which he joined from the childhood club Spjald IF.[1] He was sent on a six-month loan to Skive IK in 2008 alongside fellow talent Christian Sivebæk.[2] Upon his return to Midtjylland, he made his debut against AGF on 2 November 2008 as a starter, before being substituted in the 77th minute for Kim Christensen as his club lost 2–1.[3] He managed to become a starter for the following years and he made a total of 144 league appearances for the club.[4] He also won Player of the Year at the club for 2011.[5]
On 7 July 2014, Juelsgård signed a three-year contract with French Ligue 1 club Évian.[5]
He managed to stay with the French club for just over a year before signing a four-year agreement with Brøndby IF on 28 August 2015.[6] After a promising start at Brøndby, Juelsgård gradually slipped out of the starting line-up on the team, and he then moved to AGF, just before the summer transfer window closed in 2016.[7] He signed a three-year contract extension in June 2019.[8]
On 22 February 2022, Juelsgård was sold to Icelandic club Valur.[9] His contract was terminated in October 2022. On 12 January 2023, Juelsgård signed for Danish 1st Division side FC Fredericia on a deal until June 2024.[10]
