Drowota practiced law with Goodpasture, Carpenter, Woods & Sasser in Nashville until 1970, when he was elected chancellor of the Davidson County Chancery Court. From this position he was elevated to the Tennessee Court of Appeals in 1974. In 1980, Drowota was elected to an unexpired term on the Tennessee Supreme Court to the seat of former justice Joe Henry, who had died of a heart attack.[4]
Drowota defeated George Brown, the court's first African-American member, who had been appointed to the position by the then-Governor of TennesseeLamar Alexander, but Brown's appointment had not been confirmed by the voters.[4] Drowota won the election and was subsequently re-elected to full eight-year terms in 1982, 1990, and 1998, the last time under provisions of the Tennessee Plan. During his tenure on the Supreme Court, he was elected by his peers to two terms as chief justice.[1]
In 2006, the Tennessee Bar Association honored Drowota by establishing "The Justice Frank F. Drowota III Outstanding Judicial Service Award".[5] The award is presented annually by the organization to a Tennessee judge who has demonstrated outstanding and dedicated service to the bench and bar, with Justice Drowota as its first recipient.[6] The same year Drowota retired, he chaired the Tennessee Bar Association's committee working to ensure fair and ethical campaigns. He developed a code of conduct to govern judicial campaigns and personally contacted each judge and judicial candidate in Tennessee to encourage them to abide by the code.[6]
He served as a trustee of the Frist Foundation, Montgomery Bell Academy and the Nashville School of Law, and in 2007 he became chair-elect of the YMCA of Middle Tennessee. Drowota died in Nashville on April 15, 2018, at the age of 79.[1]