How can i create an email alert to go to my client each time the receive a new subscriber to their campaign?
I couldn't find the information you are looking for.
However, if you can get your client to use RSS you can do the following:
Click on List & Subscribers.
Select the list you want see activity from.
Click on the Subscribe link. It should read: Subscribe to list activity or export subscribers with an orange icon in front of the word Subscribe. This link will be just to the right of the list name, above the Month graph.
You may also try to use an RSS to Email service like feedmyinbox.com