You can quickly add a new project in Teamwork Projects no matter which part of your site that you're currently in, by using the Quick Add button in the top right above the search bar:

You can click the 'Add Project' option, or to speed things up even more press 'Q' on your keyboard to bring up the menu then press 'P'.

You'll be able to add details for your new project just the same as if you used the 'Add Project' button: