Bruun joined
Fortuna Hjørring from
IK Skovbakken in 2014. She made her Fortuna debut on 16 August 2014 and scored twice in a 5–1 Elitedivisionen win over
Vejle. On 8 November 2014, Bruun made her
UEFA Women's Champions League debut as a 74th minute substitute for
Nadia Nadim in a 2–1
round of 16 defeat to Swedish team
FC Rosengård. In 2016, Bruun won the
2015–16 Elitedivisionen and
Danish Women's Cup double with Fortuna. On 31 August 2018, Fortuna confirmed the transfer of Bruun to French
D1 Féminine club
Paris Saint-Germain. In her debut season, Bruun made 17 appearances in all competitions, scoring four goals. In June 2019, Bruun suffered an ACL injury that kept her out for a year. She made her competitive comeback in the delayed
Coupe de France semi-final on 2 August 2020, scoring an 84th minute winner in a 2–1 win against
Bordeaux. Seven days later she appeared as a substitute in the cup final against
Lyon. The game finished goalless after extra-time. Bruun scored during the penalty shootout but PSG lost 4–3. Later that month, Bruun appeared as a 74th minute substitute during the delayed
2019–20 UEFA Women's Champions League quarter-final against
Arsenal. She scored three minutes later, the winning goal in the single-legged 2–1 win. The following season, Bruun won the
2020–21 Division 1 Féminine title with PSG, the club's first league title, ending Lyon's 14-year streak at the top in the process. In June 2021, Bruun joined
Lyon. On 27 January 2022, Bruun made a deadline day move to English
FA Women's Super League club
Manchester United on loan for the remainder of the
2021–22 season. The spell was marred by injury, limiting Bruun to seven appearances in all competitions in which she failed to score a goal for the club. ==International career==