Høllsberg started his career at Juelsminde IF, before later moving to Vejle Boldklub at the age of 13.[1] On 25 September 2020 Vejle confirmed, that Høllsberg had signed a new contract, running from the 1 January 2021 and one-and-a-half-years onwards.[2]
After good performances in the 2021–22 pre-season with Vejle's first team, Høllsberg was rewarded with a new contract, this time until June 2024.[3] Høllsberg was also permanently promoted to the first team squad. Shortly after, on 18 July 2021, Høllsberg got his official debut for Vejle in a Danish Superliga game against Randers FC.[4] On 31 August 2022 it was confirmed, that Høllsberg had joined newly relegated Danish 2nd Division side Esbjerg fB on a season-long loan deal.[5] Høllsberg returned to Vejle at the end of the season.[6]
On 30 August 2023, Høllsberg joined newly relegated Danish 2nd Division side Fremad Amager.[7]
On 15 January 2026, Fremad Amager confirmed that they had agreed to terminate Høllsberg’s contract at his own request, as he wished to return to Jutland for personal reasons.[8] But already the following day, it was confirmed that Høllsberg had signed with the Danish 1st Division club Kolding IF on a contract running until June 2028.[9]
Following this, Høllsberg became the subject of sharp criticism, particularly from Fremad Amager’s sporting director, David Boysen, who posted an Instagram story in which he wrote, among other things: “Less than 48 hours ago, one of our players came to me and said: ‘My girlfriend is in Aarhus, and I have been through so much and don’t know what to do. I would really just like to go home, and if you are willing to listen and allow me to do so, would it be possible to receive some salary, because I don’t know when I will be paid again.’ I chose to put myself in his position and think about the person (as I have also stated publicly). Twenty-four hours after the contract termination, he has now signed a two-and-a-half-year deal with a new club. We receive nothing, and the player has received salary from us. Good style from the new club and the agents, and of course from the player himself. And I bet I am now the villain”.[10]