Additional director tenure ends immediately before the next annual general meeting, not after its conclusion. An additional director appointed by the board holds office only until the commencement of the next annual general meeting and therefore ceases to hold office immediately before that meeting. The words 'up to' are to be read as 'until,' and context indicates exclusion of the moment the meeting begins. Appointment cannot extend beyond the statutory maximum period for holding the annual general meeting, so the director's tenure is bounded both by the AGM commencement point and the statutory AGM interval.