Kovar is an unincorporated community in Bastrop County, Texas, United States. It is located within the Greater Austin metropolitan area. Kovar was named for early settler Martin Kovar, who came to the area around 1870. A church was organized by Reverend Jindrich Juren in 1894 and had 30 members in attendance, who had Czech and Moravian heritage. Agriā¦Kovar is an unincorporated community in Bastrop County, Texas, United States. It is located within the Greater Austin metropolitan area. Kovar was named for early settler Martin Kovar, who came to the area around 1870. A church was organized by Reverend Jindrich Juren in 1894 and had 30 members in attendance, who had Czech and Moravian heritage. Agriculture and a cotton gin made up the community's economy. A post office was established at Kovar in 1903 and remained in operation until 1914, with Frank Rundus as postmaster. The community never developed fully and never recorded a population, but the community's economy eventually centered on ranching.