Brinkman made his debut on May 1, 1987 in a friendly match against West-Germany. As a midfielder, he played 337 international matches for Holland, in which he scored 84 goals, making him Holland's most capped player. Brinkman surpassed the previous record holder, Cees Jan Diepeveen, in 1998. He won the Hockey World Cup in 1990 and 1998, and also the annual Champions Trophy (1996, 1998 and 2000). In the Dutch League he played for Kampong, Amsterdam H&BC and Stichtse Cricket en Hockey Club. Since the summer of 2003 he has been head coach with his former club from SCHC from Bilthoven.