According to Estonian law, you must provide a proof of ID, i.e.: your passport (or national ID card if you’re an EU citizen) and a proof of residency, i.e.: proof of address or e-residency card. If you don’t have your residency in Estonia, you might still be able to apply for a bank account, but you must provide proof that you have some interest in Estonia. Usually, a tenancy agreement, university registration or a contract of employment are widely accepted. Keep in mind, however, that e-Residency itself isn’t proof of a strong link with Estonia and banks might not deem it as sufficient to prove your status.