Tessitura does not have a native connector in Tableau Technical Support.
You can post in our Ideas section in order to get it implemented. The more votes you got the better chances you have to see it implemented.
However, there are ways to connect to data that does not have a native built-in connector.
1. The best practice solution, when working with unsupported data sources, is to mirror the unsupported data source onto a supported data source (such as SQL Server, MySQL, Oracle, etc.) and then connect to the database using the native data connection.
2.The Web Data Connector option provides a way for Tableau Desktop to connect to data that doesn't already have a connection option in Tableau Desktop.
The article below document web data connectors, what to do before you use a connector, and how to connect Tableau to a web data connector.
The Tableau Web Data Connector Community can help if you have question with building the Web Data Connector.
Hope this information help.