There shall continue to be a City Board of Alcohol Control to be composed of a chairman and two (2) other members, appointed by the Mayor and City Council, who shall be well known for their character, ability and business acumen. The Board shall be known and designated as "The City of Lincolnton Board of Alcohol Control." The chairman and the other two (2) members of the Board shall continue to serve three-year staggered terms. After their terms shall have expired, their successors in office shall serve for a period of three (3) years. Their successors or any vacancy occurring on the Board shall be named or filled by the Mayor and the City Council.