Geertsen signed with amateur club BSV after moving from Brøndby IF's U19-team in August 2010. Before coming to Brøndby, he had risen through the ranks of the Lyngby Boldklub academy. Prior to signing with BSV, he had trialled in friendly matches during the summer, where he had left a good impression. In August 2013, after three years at BSV, Geertsen signed a six-month contract with HB Køge. He made his official debut for the club on 27 August as a starter in a 3-1 Danish Cup away win over Ledøje-Smørum, with Geertsen scoring the second goal for HB Køge. Geertsen was benched during the first four league matches of the regular season, but finally made his Danish second tier debut on 9 September as a 86th-minute substitute for Thobias Ndungu Skovgaard in a 1-2 loss to Hobro IK. He made a total of eight appearances during his first sixth months at HB Køge, and signed a six-month contract extension. During the spring season of 2014, Geertsen made nine league appearances. His contract was not extended after its expiration.
On 11 July 2014, Norwegian third tier club Egersunds IK announced that they had signed a contract with Geertsen after a successful trial. After his contract with the club expired a few months later, he had a trial with FC Helsingør, without this amounting to a contract offer. Instead, Geertsen continued his career in Norway, signing with Sandnes Ulf in January 2015, a club which had recently been relegated from the Eliteserien and therefore competed in the second division. He made his official debut in the second round of the 2015 second division season, starting in a 1-1 away draw against Ranheim IL. In the summer of 2015, Geertsen signed a two-and-a-half year contract extension, keeping him a part of Sandnes Ulf until December 2017. During his time for the club, he became a regular starter and eventually also club captain. As his contract expired in December 2017, Geertsen declined a contract extension with Sandnes Ulf, citing a desire to return to Denmark. He made a total of 79 appearances scoring four goals during his three years at the club.
Return to Denmark (2018–)
A free agent, Geertsen received a number of offers from clubs in Denmark and Norway, including Bodø/Glimt and Tromsø, but he also had a trial at Nykøbing FC, who he ended up not signing with due to its long distance to Copenhagen. In March 2018, he signed with Danish third tier club Hillerød, making his first start only days after joining, in a 2-2 away draw against VSK Aarhus. Geertsen signed a contract with Lyngby Boldklub from the Danish 1st Division in July 2018 after having trained with their first team, marking a return to the club from his youth. He made his debut in the first round of competition on 29 July, starting in the centre of defense in a 1-1 home draw against Hvidovre IF. Geertsen reached promotion to the Danish Superliga during his first season at the club, in which he made 16 total appearances scoring three goals. During Martin Ørnskov's absence due to a concussion, Geertsen has emerged as club captain.
