Brewster is a city in Thomas County, Kansas, United States. As of the 2020 census, the population of the city was 291. Brewster was name…Brewster is a city in Thomas County, Kansas, United States. As of the 2020 census, the population of the city was 291. Brewster was named for L.D. Brewster, a railroad official. Brewster was a station and shipping point on the Chicago, Rock Island and Pacific Railroad.