Are there exceptions where an Estonian company does not have to submit an annual report?

There is only one exception. The annual report does not have to be submitted only if the company is registered in the second half of the year - after July 1. In this case, the company will submit an annual report for the next year and a half. At the same time, no one forbids submitting the annual report, even if you founded your company in the second half of the year.