All promotions in the New Mexico state police to the rank of sergeant shall be made after written examinations. All promotions above the rank of sergeant shall be made by the chief after concurrence and approval by the secretary. The ranks of sergeant, lieutenant and captain shall be permanent unless established as an exempt rank by the chief with the concurrence of the secretary. All promotions above the rank of captain are by executive appointment of the chief with concurrence of the secretary, and those persons shall serve at the pleasure of the chief with the concurrence of the secretary.