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 short-stay Caribbean visa to travel to the Caribbean part of the Netherlands (Aruba, Bonaire, Curaçao, Saba, St Eustatius or St Maarten).
In case you do need a short-stay Caribbean visa, please apply at the Netherlands embassy in Helsinki, Finland.