Yes, Indians are eligible to apply for the EU Blue Card to work in Estonia. However, they cannot apply for it directly from India. To apply for an EU Blue Card, you should first secure a national visa from the nearest Estonian consulate/embassy in India, after which you can enter Estonia with the national visa and then apply for an EU Blue Card.
Here is the application process for the Estonian EU Blue Card:
Step 1: Apply for a national visa
Step 2: Arrange the documents required for the visa
Step 3: Fly to Estonia on a national visa
Step 4: Apply for an EU Blue Card after entering the country
Step 5: Submit your application to the Estonian Police and Border Guard Board before the expiry of your current visa.