Salaries and other compensation of all persons who are within the unclassified service of the Kansas civil service act, and which salaries and other compensation are not fixed by statute, shall be subject to the approval of the governor and such salaries or other compensation shall not be paid until approved by the governor. The provisions of this section shall not apply to the salaries and other compensation of any officer or employee when such salary or other compensation is specifically prescribed by law, nor to officers and employees of elected state officials, officers and employees under the jurisdiction of the state board of regents, the executive secretary and other employees of the Kansas public employees retirement system that are in the unclassified service as specified under Kan. Stat. Ann. § 74-4908, and amendments thereto, officers and employees under the jurisdiction of the supreme court, legislative officers and employees or officers and employees of any agency performing functions and duties primarily for the legislative branch.