Spouse/partner rights for a residence permit
Here is a short overview of the rights of spouses/partners to obtain a residence permit or a right or residence.
In case on same sex marriage the situation is quite straightforward - the spouse can settle with the primary applicant. This is the case for third country nationals and EU citizens who's spouse is a third country national. The marriage certificate needs to be notarized and apostilled, also translated if not in English or Russian.
The same is true for same sex marriage if the marriage is concluded in a country that allows same sex marriages.
Estonia allows for same sex partners to register a partnership and the parties shall be recognized as spouses as well. From 2024 Estonia will allow for same sex marriage so quite possible same sex partnerships shall not be recognized as spouses anymore and the parties would need to get married.
Different sex couples who register their partnerships in Estonia will not benefit from the above. Meaning that for example if one party is Estonian and the other a third country national then the third country national cannot obtain a residence permit as a spouse.