Both houses of the Legislature have pro tempore (for the time being) leadership positions. At the beginning of each session, the Senate elects one member to serve as the President pro tempore when the Lieutenant Governor is absent or that office becomes vacant. A different member of the Senate - usually a senior member - is elected at the end of the session to serve as President pro tempore during the interim when the Legislature is not in session.
In the House, the Speaker simply appoints a member to preside over that chamber for a temporary period when the Speaker may be absent. Alternatively, the Speaker can appoint a Speaker pro tempore for the entire session.