Within Teamwork Projects, you can bulk set a user's project permissions across all of their projects.

Go to the 'People' section at the top of your site:

From the list of people, click on the name of the user you want to update, to view their profile.

Once you are looking at the user's profile, click the 'Options' button at the upper right of the screen and choose 'Bulk Set Permissions' from the dropdown menu:
Next you will be presented with a window that allows you to set the user's permissions across all projects they have access to.

While editing a user's permissions on one project, there is also the option to copy these permissions to all project projects they have access to.
For more information, see: Setting user permissions on a project