Implementation Regulations of Real Estate Broking Management Act Article 20

(1)A broker whose certificate is damaged or vanished shall narrate the reason and submit the documents of article 15(1)(i to iv) to the original issued institution for new certificate.(2)The municipal or the county (city) administration office shall conduct the application according to article 15( 2).
中文原文 不動產經紀業管理條例施行細則第20條
經紀人證書損壞或滅失,申請換發或補發者,應敘明其損壞或滅失之原因,檢附第十五條第一項第一款至第四款文件,向原核發機關申請之。
直轄市或縣(市)主管機關受理前項申請後,準用第十五條第二項規定辦理。

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