Is it possible to use a new Resident card from the FALA System?

No, all you need is the Jest z Gdańsk application, which in Gdańsk offers the full functionality of the Resident Card with public transport support as part of the FALA System. However, the new Resident Card with support for the FALA System (new plastic card) will also allow you to purchase public transport tickets in other cities in the Pomeranian Voivodeship where this system operates, and soon also railway tickets in the entire voivodeship.