This could get interesting, seeing as how Governor Brashear has not committed to appointing a Republican:
https://www.nbcnews.com/politics/politics-news/kentucky-governor-wont-commit-gop-appointment-mcconnell-steps-rcna103068
State laws vary when it comes to filling congressional vacancies, and the Kentucky General Assembly changed its procedures in 2021 after the GOP-controlled legislature was able to override Beshear’s veto of a bill that limited the governor's power to temporarily fill a Senate vacancy.
Under the amended law, the governor selects a Senate appointee from a list of three names submitted by the state executive committee of the outgoing senator’s affiliated party.
Kentucky state law previously permitted the governor to appoint a replacement for a vacant Senate seat until the next general House election, which occurs every two years.
In a veto statement, Beshear cited the state Constitution in suggesting that the bill “improperly and unconstitutionally" restricted the governor’s power to fill Senate vacancies.