Amends Section 4 of the Charter of the Town of Topsail Beach set out in SL 1963-67, as amended, which currently provides for any vacancy occurring in the office of mayor or commissioner to be filled for the remainder of the unexpired term by a majority vote of the remaining members of the board of commissioners. Modifies the term of persons appointed to fill such a vacancy, to now provide for the person appointed to serve the remainder of the unexpired term only if the term of office expires immediately following the next regular Town election or if the next regular Town election will be held within 90 days after the vacancy occurs. Otherwise, requires a successor to be elected at the next regularly scheduled Town election held more than 90 days after the vacancy occurs, and the person appointed to fill the vacancy serves only until the elected successor takes office, with the elected successor serving the remainder of the unexpired term. Removes the provision requiring a mayor or a member of the board of commissioners to immediately forfeit their respective office upon conviction of a crime while in office.