If a senator dies or resigns, the process for filling the vacancy depends on the state. According to the Seventeenth Amendment to the Constitution, if a vacancy occurs due to a senators death, resignation, or expulsion, state legislatures can empower the governor to appoint a replacement to complete the term or to hold office until a special election can take place. In most states, governors have the power to appoint a temporary replacement, and in most of those states, governors have free rein to appoint whomever they wish, with the appointee serving until a successor is elected to fill out the rest of the term. However, some states require a special election to fill a vacancy, and a few states require the governor to appoint a replacement of the same political party as the previous incumbent.

If a vacancy occurs in the office of United States senator, the governor shall appoint a person to fill the vacancy. That appointee shall be of the same political party as the person vacating the office and, except as provided in subsection D of this section, shall serve until the person elected at the next general election is qualified and assumes office. If a vacancy occurs more than one hundred fifty days before the next regular primary election date, the person who is appointed pursuant to subsection C of this section shall continue to serve until the vacancy is filled at the next general election.

In conclusion, the process for filling a vacancy in the Senate is complex and varies depending on the state. However, in most cases, the governor has the power to appoint a temporary replacement until a special election can take place or a successor is elected to fill out the rest of the term.