An application to transfer .EE domain can be submitted on or homepage https://www.zone.ee/en/
Transfer requires an authorization code, that can be obtained from your current registrar. If for whatever reason your current registrar don't provide the code within 5 business days, then code can be obtained from .EE domain registry - Estonian Internet Foundation.
ATTENTION! In order to successfully transfer the domain you have to sign the application, the right to representation must be established and invoice paid.
More information about signing, power of attorney and paying the invoice: https://help.zone.eu/en/Knowledgebase/Article/View/556/44/how-to-successfully-register-ee-domain
If the identity of the registrant is verified by authorizing through payment, then the transfer of the domain costs 2 euros.