Conversation so far:
What was the first job John Sherman Cooper held?
He was admitted to the bar by examination in 1928 and opened a legal practice in Somerset.
What was the first office John Sherman Cooper ran for?
After being urged into politics by his uncle, Judge Roscoe Tartar, Cooper ran unopposed for a seat in the Kentucky House of Representatives as a Republican in 1927.
How long was John Sherman Cooper in office in the Kentucky House of Representatives?
Member of the Kentucky House of Representatives from the 41st district. In office, 1928–1930

Question: Did he run for another political office after that?
Self-contained rewrite: Did John Sherman Cooper run for another political office after being Member of the Kentucky House of Representatives?