The road in front of National Library belongs to the Tallinn City Centre parking zone and parking is regulated by AS Ühisteenused.
Parking permits can be purchased from a ticket machine or through a mobile operator.

The closest car parks are:

Vabaduse väljak (Freedom Square) car park
Kaarli Puiestee car park
Citypark at the address Wismari 13/Toompuiestee 15

Please also familiarise yourselves with the general parking regulations for Tallinn, car parks and zones.