Run your subsidiary company from Estonia
Running a company in Estonia is fairly straightforward. Add to that the favourable tax system (no corporate income tax as long as the profit stays in the company) and it is easy to see why e-residency works. The same benefits would apply when you want to start a subsidiary of your existing company. While you cannot use your e-residency card to establish the subsidiary you can still use it to run the company later.
A subsidiary can be created at the notary - for this you can send notarized and apostilled powers of attorney to a lawyer to take care of the notary procedure. In addition, you would also need to send notarized and apostilled corporate documents of the mother company.
While e-residency cannot be used to open a subsidiary, you can still start a company with it online and then later sell it to the mother company. The sale of shares is also a notarized procedure (see paragraph above) but if your company has a share capital of at least 10 000 euros (fully paid in) and the articles of association allow, the share can be sold also without the notary in a rather simple procedure.
The state fee for opening a company is 190 euros if done online and 145 euros if done via a notary.If the management is not in Estonia and annual contact person service fee would apply (there are many licensed providers, our service costs 100 euros per year). If you wish to hire someone locally, you can see the labour cost examples using this tool: https://www.calkoo.com/en/salary-calculator
And finally, e-residency applications can be made here: https://e-resident.gov.ee/become-an-e-resident/