Oxford English Dictionary for interregnum:
1. Temporary authority or rule exercised during a vacancy of the throne or a suspension of the usual government.
2. The interval between the close of a king's reign and hte accession of his successor; any period during which a state is left without a ruler or with a merely provisional government.
Bill Clinton was Govenor of Arkansas from 1979 to 1981 and then, after losing one election, from 1983-1992 when he became President.