Yes, you can. Talking about employees who physically reside in Estonia, they’ll have to pay taxes there.
First of all, you must register them in the employment register on their first day at the latest. It can be done online with the e-tax system and you just need to access with your company’s login credentials.
Then, you’ll have to declare the monthly salary of your employee on the TSD, including any tax deductions or tax-free income. Of course, don’t forget to pay your share of taxes.
