Authorize.net CIM
From WHMCS Documentation
The Authorize.Net Customer Information Manager (CIM) allows you to store customers' sensitive payment information on our secure servers, simplifying your compliance with PCI regulations whilst still enabling clients to enter their card details directly onto your website and processing recurring payments.
Usage
Ensure that Setup > General Settings > Security Tab > Disable Credit Card Storage is not ticked.
This will show the credit card details form and allow clients to update the card details, and the fact you are using the CIM module will stop the details being stored in WHMCS and will send the update directly to auth.net.