Clarence is a city in western Shelby County, Missouri, United States. The population was 738 at the 2020 census. Clarence was founded in 18…Clarence is a city in western Shelby County, Missouri, United States. The population was 738 at the 2020 census. Clarence was founded in 1857. According to tradition, the community has the name of Clarence Duff, the son of a pioneer citizen. A post office called Clarence has been in operation since 1859.