Gülstorff is a product of FC Nordsjælland. In August 2020, 17-year old Gülstorff was brought into the first team squad permanently.[1][2]
However, he didn't make his official debut before Nordsjælland until August 2022, where he was involved from the start in a Danish Cup match against BK Frem.[3][4]
Gülstorff didn't make his Danish Superliga debut until December 3, 2023, when he had to step in as third goalkeeper, as both the first and second goalkeepers were unavailable. He was therefore given the chance from the start against OB; a match that ended 1-1.[5][6]
Aalesunds
On September 1, 2024 it was confirmed that Gülstorff had been loaned to Norwegian Norwegian First Division club Aalesunds for the rest of the year, with an option to buy.[7][8]