Any person who shall have been in good faith a resident of said library district for thirty (30) days prior to the date of any district meeting or other election and who possesses the qualifications of a voter at a general election shall be entitled to vote at said meeting or at any bond election. Every library district so created shall be governed by a board of seven (7) directors who shall be qualified voters of such library district. The board of directors shall elect one of their number as chairman of said board and shall also elect from the members of said board a secretary and a treasurer and such other officers as they deem necessary. At each annual meeting, upon the expiration of the term of any director, his or her successor shall be elected for a term of four (4) years, expiring on the first Tuesday of April of the fourth year following his or her election. Vacancies in said board of directors accruing by death, removal, resignation or otherwise shall be filled for the unexpired term by appointment made by the chairman of said board, by and with the endorsement and approval of a majority of the remaining board members, and shall be for the unexpired term in like manner as the original elections.