Within Teamwork Projects, you can quickly add a new project no matter which part of your site you are currently in, by using the quick add + button in the top right above the search bar.
You can select the + and click the Project option, or you can use keyboard shortcuts by pressing q on your keyboard to bring up the menu then press p.
You will be able to add details for your new project just the same as if you used the Add Project button.
For more information, see: Using the Quick Add Menu