Conversation so far:
What was the first job John Sherman Cooper held?
After being urged into politics by his uncle, Judge Roscoe Tartar.
What was the first office he ran for?
Cooper ran unopposed for a seat in the Kentucky House of Representatives as a Republican in 1927.
How long was he in office?
CANNOTANSWER.

Question: Did he run for another political office after that?
Self-contained rewrite: Did John Sherman Cooper run for another political office after his run for the Kentucky House of Representatives in 1927?