Local Government Act Article 83

When the term of office for a councilor of the special municipality, mayor of the special municipality, county/city councilor, magistrate/mayor, township/city representative, a mayor of the township/city, or chief of village expires or when such an office becomes vacant and thus in need of an election or supplementary election, such an election or supplementary election may be postponed under extraordinary circumstances.The aforementioned postponement of the election or supplementary election of a councilor of the special municipality, mayor of the special municipality, county/city councilor, or magistrate/mayor shall be carried out upon approval by the Executive Yuan or Ministry of the Interior, respectively.In accordance with Paragraph 1, the aforementioned postponement of the election or supplementary election of a township/city representative, mayor of the township/city, or chief of village shall be carried out upon approval by the respective special municipality or county/city government.When an election is postponed in accordance with the preceding three paragraphs, the current term of office shall be lengthened on the basis of the prevailing circumstances. If the office should become vacant during the lengthened term, no supplementary election shall be held.
中文原文 地方制度法第83條
直轄市議員、直轄市長、縣(市)議員、縣(市)長、鄉(鎮、市)民代表、鄉(鎮、市)長及村(里)長任期屆滿或出缺應改選或補選時,如因特殊事故,得延期辦理改選或補選。
直轄市議員、直轄市長、縣(市)議員、縣(市)長依前項延期辦理改選或補選,分別由行政院、內政部核准後辦理。
鄉(鎮、市)民代表、鄉(鎮、市)長、村(里)長依第一項規定延期辦理改選或補選,由各該直轄市政府、縣(市)政府核准後辦理。
依前三項規定延期辦理改選時,其本屆任期依事實延長之。
如於延長任期中出缺時,均不補選。

English translation for reference only; the Chinese text prevails. Not legal advice.