Who appoints a new member to fill an unexpired board term?

The correct answer is that the governor appoints a new member to fill an unexpired board term. In the context of many state boards, including those related to public security and regulatory agencies, the governor typically holds the authority to appoint individuals to fill vacancies. This process ensures that the appointed members align with the state's legal and administrative framework, reflecting the priorities and goals of the current administration.

Board members often play a crucial role in overseeing the functions and operations of an agency, making it essential that vacancies are filled efficiently and in a manner that maintains the continuity and integrity of governance. The governor’s appointments can further influence the policies and direction of the board, ensuring it adheres to the state’s vision and regulatory needs.

The other options, while they might seem plausible in different contexts, do not reflect the established procedure regarding appointments for board vacancies in this specific case.