Final answer:
When a Senator dies or resigns, the state governor can appoint a temporary replacement, with a special election later held to elect a new senator for the rest of the term, as per the 17th Amendment.
Step-by-step explanation:
If a Senator dies or resigns while in office, the state governor has the authority to appoint a replacement. According to the 17th Amendment of the U.S. Constitution, when vacancies occur in the Senate, the executive authority of the state shall issue writs of election to fill such vacancies. Additionally, the state legislature may allow the governor to make temporary appointments until a special election can be held.
The procedure is that the governor appoints a temporary senator who will serve until a special election is organized. This special election is conducted to elect a new senator who will serve for the remainder of the term. Notably, all but four states—Massachusetts, Oregon, Wisconsin, and Oklahoma—permit such temporary appointments, with the special election following according to the state's directed timetable.