There are 2 US Post Offices in Clay County serving a total of 5,278 residents equating to 2,639 residents per post office. It's estimated that approximately 8,424 packages are handled across the 2 county post offices annually. Clay County is a county located in the U.S. state of Tennessee. As of the 2010 census, the population was 7,861. Its county seat and only incorporated city is Celina. Clay County is named in honor of American statesman Henry Clay, member of the United States Senate from Kentucky and United States Secretary of State in the 19th century."