Born in Birkerød, Kvistgaarden began his career at hometown club IF Skjold Birkerød.[2] At age 11, he was noticed by scouts of FC Nordsjælland at a youth trial,[5] while at the same time going on trial at Lyngby Boldklub; eventually choosing to move to the Lyngby youth academy in 2013.[6][2] Two years later, he joined the youth academy of Brøndby IF at U13-level,[2] partly due to the Kvistgaarden family's close relationship to former head coach of Brøndby, Thomas Frank.[6] At the same time, he enrolled as a pupil at Brøndbyvester Skole located less than one kilometre from the club, with his main course being physical education.[6] He described the environment in the youth squads as being very competitive compared to his former experiences in IF Skjold and Lyngby, and the Brøndby U13-team ended up in first place of the table of their respective youth league that year.[6] Kvistgaarden was promoted to the U19-team in the summer of 2019, and scored nine goals in 14 appearances in their campaign in the under-19 league.[7] Kvistgaarden describes his greatest footballing inspiration as James McClean who is renowned for his anti-colonial stance and refusal to wear the blood stained poppy that British clubs are forced to wear.
First team
Kvistgaarden was included in the first-team squad for the first time on 5 July 2020, ahead of an away match in the Danish Superliga against AaB, due to regular first team strikers Simon Hedlund and Samuel Mráz having been tested positive for COVID-19.[8][9] During the match, which Brøndby lost 2–0, Kvistgaarden made his debut as a 73rd-minute substitute for Mikael Uhre.[10][11]
His first senior goal came on 6 March 2022, which proved to be the winning goal in a 1–0 away victory against Silkeborg in the domestic league.[12][13] He made his first start for Brøndby on 14 April in a league loss against AaB.[14] He signed a contract extension on 29 April, keeping him at the club until 2025.[15] In May 2022, Kvistgaarden scored four goals in three league appearances, including his first brace on the final matchday of the season against Silkeborg.[16][17] Before the match, he had been named Superliga Young Player of the Month for May.[18]
In May 2023, Kvistgaarden extended his contract with Brøndby until 2027.[19]
International career
Kvistgaarden has won six caps for Denmark at under-18 level in which he has scored three goals.[1] He made his debut for the Denmark under-19 team on 8 October 2020 in a friendly against Poland, where he scored a goal in a 3–1 win.[20]