The board of police commissioners shall elect one of its number to be chairman and one member to be clerk and shall hold regular meetings and keep records of the same. Meetings shall be held upon the call of the chairman or of a majority of the members of the board. A majority of the members of the board shall constitute a quorum. In the event of any vacancy upon the board, the board of selectmen shall have authority by majority vote to fill such vacancy until the next town election, at which election a member shall be elected for the unexpired portion of the term.