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Money Laundering and Terrorist Financing Prevention Act in English You can find here:
https://www.riigiteataja.ee/en/eli/ee/Riigikogu/act/517112017003/consolide

§ 2.  Application of Act
 (1) This Act applies to the economic and professional activities of the following persons: 1) credit institutions;
 2) financial institutions;
….
10) providers of a service of exchanging a virtual currency against a fiat currency;
 11) providers of a virtual currency wallet service;

§ 70.  Authorisation obligation
 (1) An undertaking is required to have authorisation for operating in the following areas of activity:
 1) operating as a financial institution;
 2) providing trust and company services;
 3) providing pawnbroking services;
4) providing services of exchanging a virtual currency against a fiat currency;
 5) providing a virtual currency wallet service;
 6) buying-in or wholesale of precious metals, precious metal articles or precious stones, except precious metals and precious metal articles used for production, scientific or medical purposes.