The Police clearance certificate/Certificate of good conduct is issued by the Estonian Punishment Register: http://www.rik.ee/en/punishment-register.
In case you have an ID-card (with pin-codes and an ID-card reader) it is possible to apply for it online: www.e-toimik.ee.
It is also possible to apply for it by post or e-mail. An application form (45 KB, DOC) has to be sent to the following e-mail firstname.lastname@example.org or by post Karistusregister, Lõkke 4, 10122, Tallinn, Estonia.
The certificate is in Estonian language and in case you order it yourself it will be issued for free.
You can apply for a consul’s statement in English from the Embassy by post. In order to do so please send us your original certificate of good conduct (in Estonian), copy of your passport or ID-card and the state fee £27. The state fee has to be paid by Postal Order (cheque from a post office; payable to: Estonian Embassy)..