Not in Kentucky. Special election.
If McConnell lives past August 3rd, I understand that there will not be a special election. He decided not to run for reelection, and there is a November race between a Republican (Andy Barr) and a Democrat (Charles Booker). Thomas Massie is a wild card; if Kentucky has a “sore loser” law, that would preclude him from running as an independent from his House seat. However, such a law would not prevent him from running for the Senate. Kentucky has not had a Democratic Senator since 1999. Booker lost in 2022 to Rand Paul by over 23 percentage points, so unless Massie jumps in the race for spite, this is a safe GOP seat.