Remmer joined the first-team squad at Copenhagen in the beginning of 2012–13 season, together with Andreas Cornelius and Jakob Busk.[1] Remmer was expected to become Lars Jacobsen's successor on the right back position.[2]
Remmer gained his first Superliga match on 4 August 2012, when he was in the starting line-up against Esbjerg fB at Blue Water Arena in Esbjerg. 33 minutes into his debut, he assisted on Martin Vingaard's 1-0 goal.
Molde
On 10 August 2016, Remmer signed a three-year contract with Norwegian Tippeligaen side Molde FK.[3] He made his debut for the club in a 2–0 away win against Aalesund on 14 August 2016. On 23 May 2019, Remmer scored his first goal in his senior career in Molde's 4–0 win against Sunndal in the Norwegian Cup second round.[4]
Westerlo
On 16 July 2019, it was confirmed that Remmer had moved to Belgian club Westerlo on a three-year contract.[5]
SønderjyskE
On 7 June 2022, Remmer returned to his homeland, when he joined newly relegated Danish 1st Division club SønderjyskE on a deal until June 2024.[6]
In May 2024, SønderjyskE announced that Remmer will leave the club, when his contract expires.[7]
In September 2023, Remmer was hospitalised after contracting meningitis, spending ten days in intensive care unit.[9] He made a full recovery, and returned to competitive football in March 2024.[10]