On the first Tuesday in April after the expiration of two years from the date of the election of the first board of trustees for respective terms of two, four and six years each, an election shall be called and held by the board of trustees and every two years thereafter shall be so called and held for the purpose of electing a trustee who shall serve for a term of six years and until his successor shall have been elected and qualified to fill the office of the trustee whose term may then expire and any vacancy then existing in the membership of said board shall be filled at such election.