Except as otherwise provided by statute, on or before March 1, 1975, and quadrennially thereafter, the Governor shall, with the advice and consent of either house of the General Assembly, appoint each department head in the manner prescribed by § 4-7 and § 4-8, to serve at the pleasure of the Governor but no longer than four years from the first day of March in the year of his appointment, unless reappointed under the provisions of said sections. In the event a department head is not appointed or an incumbent reappointed in the manner prescribed in § 4-8 prior to the first day of March in the year of the appointment, the incumbent may serve beyond that date but not later than the tenth day of March in that year.