Honolulu Mayor -- Unexpired Term -- One Year or More in office

City Charter §5-107

(Vacancy is to be) (f)illed by a special election to be called by the Council within 10 days and to be held within 60 days after occurrence of the vacancy. If any special or general election is to be held in the City after 30 days and within 180 days after the occurrence of the vacancy, the election shall be held in conjunction with such other election.

(Both the Primary Election September 18 and the General Election November 2 fall in between the 30 to 180 day rule, but only the Primary Election also falls within the “60 days” rule if Hannemann resigns as expected on July 20.)   

Pending Election: Filled by the Managing Director, or if no Managing Director or Managing Director is unable to act, the Chief Budget Officer shall then act as Mayor.

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SOURCE: http://hawaii.gov/elections/factsheets/html/fsbo118.htm

RESIGN TO RUN LAW:

“A person who is required to resign from a state or county office currently held must do so no later than when nomination papers for the office sought are filed.”

SOURCE: FACTSHEET CANDIDATE RESIGNATION REQUIREMENTS HAWAII ELECTIVE