Non-residents not registered in the commercial register in Estonia and operating in Estonia through a permanent establishment or non-residents not having a permanent establishment but being employers in Estonia have to register with the Estonian Tax and Customs Board. Likewise, non-resident employees and recipients of payments not having an Estonian personal identification code have to be registered with the Estonian Tax and Customs Board.
Closer look: https://www.emta.ee/en/business-client/registration-business/non-residents-e-residents/registration-non-resident