Unless otherwise provided in the articles or bylaws and except for a vacancy created by the removal of a director, vacancies on the board may be filled by approval of a majority of the remaining directors on the board. Corp. Code §7224(a). This general principle is also described in Robert's Rules of Order:

The power to appoint or elect persons to any office or board carries with it the power to accept their resignations, and also the power to fill any vacancy occurring in it, unless the bylaws expressly provide otherwise. (Robert's Rules, 11th ed., p. 467.)

Term of Office. The appointed director's term of office shall be as provided for in the bylaws. Appointing a new director does not affect existing officer terms of office. (See difference between officers and directors.)

Vote by Resigning Director. Because a director retains all of the authority of a director until such time as the resignation becomes effective, the resigning director may participate in the selection of his or her replacement, provided the selection takes place prior to the effective date of the resignation. Mayo v. Interment Properties.

Open Session. While interviewing candidates may be done privately, the appointment of a director should be done in open session. Voting to fill a vacancy does not fall into any of the approved categories for executive session. The vote to fill an empty seat needs to be on the meeting's agenda.

Failure to Fill Position. If the board fails or refuses to fill an empty position, the membership may elect a director at any time to fill the position.Corp. Code §7224(b). The process is initiated by filing a petition with the board for a special membership meeting to fill the vacant seat.

Less Than a Quorum. If there is more than one vacant seat such that the remaining directors are less than a quorum, the remaining directors cannot conduct any business except to appoint other directors to the board.