Gov. Steve Beshear is relying on a 1942 law combined with general ignorance of changes in the Kentucky Constitution from 1992 to appoint a new lieutenant governor today after Jerry Abramson resigned to work in the Obama Administration.
KRS 63.190, enacted in 1942, states "In every case where there is no provision of law for the filling of a vacancy in any office, the vacancy shall be filled by an appointment by the Governor."
But several changes in the Constitution enacted 1992 did speak to the issue and since a gubernatorial vacancy had not happened under those rules until today, the issue hasn't been thoroughly explored. When you look at the relevant constitutional sections, it becomes clear Beshear can't override the will of the voters or the Kentucky Constitution by replacing a duly elected lieutenant governor on a whim.
Section 70 of the Kentucky Constitution states: "The Governor and Lieutenant Governor shall be elected for the term of four years by the qualified voters of the state. They shall be elected jointly by the casting by each voter of a single vote applicable to both offices, as shall be provided by law."
This section combined the offices at the head of Kentucky's executive branch for the first time in history. The lieutenant governor can't attain that office by his own election. He (or she) gains the office by election with a candidate for governor. The office of governor is not filled without both a governor and lieutenant governor. So this brings in Section 85.
Section 85 of the Kentucky Constitution states: "And if, during the vacancy of the office of Governor, the Lieutenant Governor shall be impeached and removed from office, refuse to qualify, resign, or die, the President of the Senate shall in like manner administer the government."
The office of Governor as defined by Section 70 became partially vacant when Abramson resigned. Section 85 describes how such a vacancy is to be remedied. Senate President Stivers should become Kentucky's Lieutenant Governor.