**Before you add a client to an existing Project, make sure that the client already exists as a 1) Contact and an 2) Entity.
Go to the desired Project > select the "down arrow / caret" (right of Project name) > select "Edit Clients"
On the drawer that opens up from the right side of the screen, add the proper client to the Project.
Once the client has been added, select "Assign to all". This adds the client to all Tasks within the Project.
Lastly, it's best practice to notify the client that they've been successfully added and assigned to the Project.
And that's it!