While, it's not possible to directly integrate with Tessitura, you can sync users between us and them using a combination of Webhooks and our APIs.
You'll definitely need to hire a third party developer for this level of customization.
A developer would need to use the Tessitura API and build a small application between our two softwares to take new users/purchases made in Tessitura and create the user in Uscreen while granting the correct access.
Users added first into Uscreen could also be sent to Tessitura using our webhooks. Again though, you'll need that small application built between us or perhaps you can think about using Zapier's webhook functionality.