The Netherlands embassy in Tallinn does not issue visa.
Estonia is part of the Schengen area. Do you have the nationality of Estonia? Or do you have a valid Schengen visa or a residence permit for Estonia? Then you do not need to apply for a long-stay Caribbean visa to travel to the Caribbean part of the Netherlands (Aruba, Bonaire, Curaçao, Saba, St Eustatius or St Maarten).
If you want to stay in the Caribbean parts of the Kingdom for longer than 90 days, you will normally need a residence permit.
In case you do need a short-stay Caribbean visa, please apply at the Netherlands embassy in Helsinki, Finland.