He attended public schools and earned his Bachelor of Science degree in pharmacy from Southwestern Oklahoma State University in Weatherford, Oklahoma in 1968.
After college graduation, Brewster moved to Colleyville, Texas, where, as a licensed pharmacist, he owned and operated the Colleyville Drug until 1977. In 1968 he also began a career as a cattleman and rancher when he started Brewster Angus Farms. As well as owning a real estate business.
In the late 1970s he settled in Marietta, Oklahoma.
In 1983, Brewster was elected to a seat in the Oklahoma House of Representatives. He was re-elected in 1984, and served until 1990, when he chose, instead, to run for an open seat to the United States. House of Representatives (District 3 — then Congressman Wes Watkins had decided to retire from Congress and run for Governor of Oklahoma).
He was re-elected in 1992, and then again in 1994, serving from January 3, 1991 to January 3, 1997. Brewster decided to retire from Congress in 1996, after Former Congressman Wes Watkins began lining up support.
He was mentioned as a possible Democratic candidate for governor in 1998, but declined to run for the nomination.
After he left Congress, Brewster joined R. Duffy Wall and Associates, a Washington, District of Columbia, lobbying firm, and in 2001 he served as president and chief operating officer of this firm. He also was Chief Executive Officer and Chairman of Capitol Hill Consulting Group.
He was initiated into Tau Kappa Epsilon Fraternity, and was a member of the United States Army Reserves from 1966 to 1971.