He previously served in fast attack craft units, and in staff positions, and has a degree in education from the University of the Bundeswehr Hamburg.

Brinkmann joined the German Navy as an enlisted member in 1976, serving on the deck crew of ships in the 7th Fast Attack Squadron (7.

He served with the squadron until 1985, when he was appointed as adjutant of the Schleswig-Holstein Territorial Command, and German liaison officer to Allied Forces Northern Europe.

He then served as operations officer (S3) and deputy commander of the 2nd Fast Attack Squadron based in Kappeln.

From 2010 to 2012, he served as deputy director of a Federal Ministry of Defence department in Bonn, and from 2012 to 2014, he served as deputy commander of the Bundeswehr Operations Command (responsible for Bundeswehr operational missions, including foreign deployments).