I think you are misunderstanding your current account. "Thunderbird" is a program that runs on your local computer that interacts with your email service (Gmail, Yahoo, Comcast, etc.) There is no "Thunderbird account", that is, there is no Thunderbird email host. Your email address may identify your true email service.

Thunderbird, the program, can hold multiple email accounts. If you decide to subscribe to Gmail or Yahoo or whoever, you can simply add those accounts to Thunderbird. You can then discontinue your old service, or maybe have that email forwarded to your new address (that would best be done at the web mail page for your current service.)