In 2002, Brewster was invited to play in his first World championship. He was an alternate for the Warwick Smith team which won a bronze medal in 2002. Brewster won his first Scottish men's title in 2011, and represented Scotland at the 2011 Ford World Men's Curling Championship, finishing second in the round robin and winning the silver in the final against Canada's Jeff Stoughton. In 2012 he again won silver, this time losing in the final against Canadian skip Glenn Howard.