At the end of the war, Maverick returned to San Antonio, where he earned a law degree at St. Mary's University in 1949.
A committed liberal, he became well known during his term in office as a supporter of organized labor and civil rights for African Americans and an opponent of the persecution of suspected communists during the Red Scare.
Having split the liberal vote, thus allowing the conservative Blakley to make the runoff against Republican John Tower (who received 31 percent in the initial round and was narrowly elected in the runoff), Maverick and Gonzalez, a friend and fellow San Antonian, stopped speaking to one another for almost the next twenty years.
In 1964, in Stanford v. Texas, he represented John W. Stanford Jr., a bookstore owner and Communist Party USA member convicted of sedition for selling books authored by Karl Marx, Jean-Paul Sartre, Pope John XXIII, and Supreme Court Associate Justice Hugo Black.
In mid-January 2003, Maverick filed his last column, which condemned the imminent Iraq War as "unjust," and entered a local hospital to be treated for kidney disease.