Is it possible to set up an email address with a white list so that I can restrict access to only those people on that list? Also – would I need to establish a new domain to accomplish this or could I just add another email address to an existing domain? Thank you for your assistance.
Your question is actually quite complex. Even that cPanel offers email filtering functionality it only allows you to restrict the access for specific addresses, blacklist IP addresses or block specific content not to be delivered to you. Since the result you are looking for is not quite commonly needed you should find another way to achieve it due to the fact that cPanel does not offer an email whitelisting feature.
However you can find more information on the Email Filtering in the official cPanel documentation here.