I decided to email the three main banks (LHV Pank, SEB and Swedbank) in Estonia regarding their status on remote bank account opening since the legislation was approved. I will keep this thread updated after I receive email replies.
LHV Pank: Not supported. No timeline for support.
SEB: Only supported for existing personal account customers. No timeline for support.
Swedbank: Not possible. No indication whether or not they plan to allow it in the future.
Email response from LHV Pank (emphasis theirs):
Thank you for your interest in opening a bank account with LHV Pank.
To have an account in LHV Pank you need to have some kind of connection with Estonia through partners, customers or someone similar; for private persons a scholarship from Estonian university, working agreement with Estonian company or something similar would do. Also, you need to fill in the application forms and specify other essentials.
The opening of the account is decided on in committee, and this may take up to 7 working days. We will look through your application and then inform you about our decision. Once your application has been approved, we will be ready to welcome you at our client office in Tartu or in Tallinn. You have to visit one of our offices for identification and signing all the necessary documents as we can't offer account opening on a remote basis. At the moment we have no information when will be possible to identify remotely.
Email response from Swedbank:
It is not possible to open a bank account remotely in Swedbank Estonia via e-resident card.
Email response from SEB:
Thank you for your letter and for being interested in opening an account in our bank.
For opening an account you will need to turn to one of our offices. At the moment we only open account remotely for our current customers who already have a personal Internet Bank contract with us.
Our branch locations and opening hours you will find from address
http://www.seb.ee/en/bank-offices-and-b ... ffices-seb.
Unfortunately at the moment we have no information when this solution will be available or what services we can offer for our new private customers.
I hope my answer was helpful and we are waiting for you in our branch.
Update 08/05/2017: Added response from Swedbank.
Update 08/05/2017 #2: Added response from SEB.