Brinch is a product of Esbjerg and which he joined at the age of five. He was promoted to the first team squad in the summer 2014 alongside two other U19 players.[1]
In December 2015, Brinch extended his contract for the rest of the season.[4] He played 13 league matches for the club in the 2015/16 season and extended his contract once again in April 2016, this time until 2019.[5]
FC Fredericia
On 1 September 2021, Brinch joined fellow league club, FC Fredericia, on a deal until June 2023.[6] When the contract expired in June 2023, Brinch and Fredericia extended the agreement until June 2025.[7]
On August 29, 2024, Fredericia confirmed that they had terminated the agreement with Brinch, as he had struggled for playing time in the team over the past year.[8]
Fremad Amager
On transfer deadline day, August 30, 2024, Brinch moved to Danish 2nd Division side Fremad Amager.[9] The very next day, on August 31, 2024, he made his debut in a 0-4 defeat to Middelfart Boldklub when he was substituted after 33 minutes of play.[10]