Wright served as a judge of the circuit court of Tennessee, and then as a chancellor and judge of the Tennessee Supreme Court. He practiced law in Nashville in 1885 and 1886. He was an unsuccessful candidate as an Anti-Repudiation Democrat for governor of Tennessee in 1880. He was chairman of the Northwest Indian Commission in 1886 and a member of the commission to treat with the Great Sioux Nation in Dakota. He was appointed to the law division of the General Land Office in 1887 and served until his death.