The Secretary of State shall, after consultation with an authority’s chairman or chairman designate (if there is a person holding, or as the case may be designated to hold, that office) make the first appointment of their chief executive on such terms and conditions as the Secretary of State may, with the consent of the Treasury, determine; and the authority may, with the approval of the Secretary of State, make subsequent appointments to the office of chief executive on such terms and conditions as they may with the approval of the Secretary of State, given with the consent of the Treasury, determine.