[1] On 5 April 2008, he made his professional debut when he came on as a substitute on for Mike Jensen in the 82nd minute in a 3–1 victory against AC Horsens.
After six months in Brøndby again without an appearance, Kanstrup was loaned out again, this time to second-tier 1st Division club Brønshøj Boldklub.
[5] In the 2012–13 season he played three more times for Brønshøj and was even named team captain, before moving to division rivals Fredericia.
[2] For the second half of the 2013–14 season, Kanstrup was loaned by Superliga club SønderjyskE and immediately became a regular starter in defense, making his debut in the 0–4 away win over Vestsjælland.
[15] After only six months at the club, he was named team captain after the departure of Morten "Duncan" Rasmussen, which was the "natural choice" according to head coach David Nielsen.
[2] In January 2019, he left Denmark and joined the Turkish Süper Lig club Büyükşehir Belediye Erzurumspor.
[20] On 27 August 2021, Kanstrup was loaned out to Danish 1st Division club Fremad Amager for the rest of the season.
[23] After leaving Fremad Amager, Kanstrup signed for Denmark Series side Brønshøj Boldklub in July 2023: a club he had already played for previously, in 2011-2012.