Find your newly added application in the integration menu and open it again by clicking on the listed application. Before you can use the Application, Teamleader wants to verify that you as a user are authorized to use the API.
The Authorize button will open a new window, in which you will need to enter your Teamleader login credentials. Afterwards you will need to allow the connection to be created.
If the process was successful, the connection can be tested, and will return a green check mark.