Final answer:
When a Commission vacancy occurs in the U.S. Senate, the governor usually issues writs of election following the 17th Amendment, and may make temporary appointments until a special election occurs. For a federal commission, the President appoints, and the Senate confirms, new members. State legislatures may have particular rules that govern these processes.
Step-by-step explanation:
In the event of a Commission vacancy, particularly referencing a vacancy in the representation of any state in the U.S. Senate, the process for appointing a new member is largely determined by state procedures consistent with federal guidelines. According to the 17th Amendment, when such vacancies occur, the executive authority of the state, usually the governor, is responsible for issuing writs of election to fill the vacancy. Meanwhile, the state legislature may grant the executive authority the power to make temporary appointments until a special election can be held for the people to elect a new senator as directed by the legislature.
If the office of the lieutenant governor becomes vacant, the successor is elected by the Senate members. In some cases, the president pro tempore of the Senate may perform the duties temporarily. When it comes to agency leadership, such as a federal commission, the President of the United States appoints commissioners and the U.S. Senate confirms them. The state's processes may vary, but they typically follow the guidelines of federal amendments and related laws governing such vacancies.