The Governor shall appoint with the approval of a majority of the Legislature, all persons whose offices are established by the Constitution, or which may be created by law, and whose appointment or election is not otherwise by law or herein provided for; and no such person shall be appointed or elected by the Legislature. The Governor shall have power to remove, for cause and after a public hearing, any person whom he may appoint for a term except officers provided for in Article V of the Constitution, and he may declare his office vacant, and fill the same as herein provided as in other cases of vacancy. The Governor shall have power to remove any other person whom he appoints at any time and for any reason.