Within Teamwork, you can change the email address associated with your subscription invoices.
The default email address for your invoice and subscription emails will be your site owner's email address when you subscribe to a plan.
To change it to another email address, click your profile avatar in the bottom left of your site and select Subscription from the pop-out menu.

In the Subscription area, click the Update Payment Details button under your current plan summary.

This will bring you to the Billing Details view where you can enter in a new contact email address.
Click Update to save your changes.

Legacy plans
For some legacy subscription plans, the steps to update differ. Click View Invoices near the top right of your Subscription area to view your invoices.

This will bring you to the invoice history tab. At the bottom of the list of payments, you will see a link to Choose another email address.

A pop-up modal will open where you can enter a new contact email address. Click Update Email Address to save your changes.

Note: Only site administrators in the owner company can access this area.
For more information, see: Adding More Users to Your Subscription on Per-user Plans