Clarence is a town located in the northeastern part of Erie County, New York, United States. The population was 26,123 at the 2000 census. Clarence is also the name of a postal district in the south part of the town with ZIP code 14031. It is named after the House of Clarence in England. The Town of Clarence is in the northeast part of the county. The town is northeast of Buffalo. There are no incorporated villages within the town.