La. R.S. 11:512

Any vacancy on the board of trustees shall be filled by the board of trustees for the unexpired term of office, provided that if the unexpired term is for a period of more than two years, the appointment shall be for the period intervening until January first following the next regular election, at which election a member shall be elected to fill the unexpired portion of the term in accordance with the provisions of this Part. The above does not apply to the trustee who is a retired member of the system, as his successor would be appointed by the executive board of the retired state employees association.