"Section 4.06. Term of Office. Each Director shall hold office for a term of three (3) years. Directors may be reelected for two (2) succeeding terms. Whenever a vacancy occurs in the membership of the Board because of death, resignation, removal, or inability to act, such vacancy may be filled by an appointee or appointees selected by a majority of the remaining members of the Board. Such appointee or appointees shall hold office during the unexpired term or terms of their predecessor or predecessors."
No, bylaws do not say anything about serving until successor is selected.
An additional question - if a term expires, does that a vacancy? From 4.06 above, I don't interpret that to be the case.