Act to Establish the National Culture and Arts Foundation Article 9

Where directors or supervisors quit, die, where the position they hold at their respective government agency changes, or where they are otherwise unable to carry out their duties, the supervisory agency shall request the Premier to make an appointment to fill the vacancy.Those appointed to fill vacant seats shall serve within the original term of the director or supervisor.
中文原文 國家文化藝術基金會設置條例第9條
董事、監事因辭職、死亡、代表該機關之職務變更或因故無法執行職務時,應予解聘;其所遺缺額,由主管機關提請行政院院長補聘之。
補聘之董事、監事,其聘期以補足原任者之聘期為止。

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