As Timmer noted, you can set a tournament to be your "default" tournament, and be automatically loaded every time you start the TD. Settings window -> Preferences tab -> Config Files button
This is a little different than just loading the last tournament. When you've got a "default" tournament, it will be loaded automatically when the TD starts, but it will be reset back to the start and players won't be bought-in. It's intended to be a tournament template.
If you're simply looking to start where you last left off, there's currently no way to do that. But I will add it to my to-do list.