Brinkman debuted for the senior national team in 2015, in a test match against South Africa, in Cape Town. Brinkman represented the Netherlands at the 2018 Men's Hockey Champions Trophy in Breda, Netherlands, where the team won a bronze medal. In October 2018, he was named in the Dutch squad for the 2018 World Cup, which meant he was about to make his World Cup debut. He played in all seven matches and scored four goals, they eventually los in the final to Belgium. In June 2019, he was selected in the Netherlands squad for the 2019 EuroHockey Championship. They won the bronze medal by defeating Germany 4–0.