Come posso utilizzare la mia tessera degli autobus Tartu a Tallinn?

You can buy a ticket the same way as in Tartu. So add some money onto the card and use the validator.

If for whatever reason you don’t want to add money then you can buy a ticket from the front door validator using a contactless bank card.

https://www.tallinn.ee/en/pilet/public-transport-tickets-tallinn