If the regularly elected lieutenant governor succeeds to the office of governor as provided in the constitution and thereafter, during the same regular gubernatorial term, the office of governor again becomes vacant, the appointed lieutenant governor succeeds to the office of acting governor until a special election to elect a governor and lieutenant governor is held.
AS 44.19.044
Special election in case of second vacancy in office of governor
Official source: Alaska State Legislature. Reproduced from public-domain Alaska statutes; confirm against the official source for the current text. Not legal advice.