There is no such thing in Estonia as a special “work permit”. You can work here if your short‐term employment is registered by your employer and your stay here is legal (e.g. you have a D-visa) or when you have a valid (temporary) residence permit for working.
With Citizen of the EU, the EEA (Iceland, Liechtenstein and Norway)
If you want to work in Estonia for more than 3 months, you just need to register as an Estonian resident in the Population Register of Estonia during the first 3 months of your stay.
With Non-EU
If you would like to work in Estonia for a short time (up to 6 months in a year), you should apply for a D-visa. Before applying for a D-visa, your employer should register your short-term employment with the Estonian Police and Border Guard Board.
For longer than 6 months, you need to apply for a residence permit. At first, you have to apply for a temporary residence permit (for work up to 2 years with your first permit). After having lived in Estonia for 5 years on a temporary residence permit, you can then apply for a permanent residence permit.
If you wish to settle in Estonia permanently, you can also apply for a long-term temporary residence permit created to make settling and fulfilling the required criteria for a permanent residence permit easier.
Country : Estonia