Can not restore Gmail on mac book pro running OS El Capitain

That is expected behavior.

A number of Google services including Mail now require newer versions of the macOS and, as a result, the Apple Mail app. El Capitan is quite old.

You can contnue to acces mail throguh a browser, or shop for a new computer.

However, before shopping, please tell us which Macbook Pro sub-model (the bit containing a YEAR) you have.

If it is a Mid 2009, it is hardware-contrained to no higher than macOS 10.11 El Capitan

If a Mid 2010 or any 2011 model, it can run up to macOS 10.13 High Sierra.

IF a Mid 2012, it can run up to macOS 10.15 Catalina, which I believe Google still supports.

If yours is newer than 2012 please post the sub-model so we can better assess your upgrade path, if any.

In macOS 10.11, your sub-model is always available from "About this Mac..." Example:

The red arrow show where the important sub-model designator is located in El Capitan.

⚠️ Security Note: For security reasons, please DO NOT post a serial number here.

Hi there andygld,

If you are unable to add this specific account to the Mail app on your MacBook Pro, we would recommend reaching out to the email provider. They would be the best equipped to check compatibility and investigate this issue further. Contact them here: Gmail Help

Take care.

My advice would be to use Gmail as it's meant to be used, by using the web page, not a mail client. Gmail's labelling, among other things is quite different than using Mail and its folders. That would solve your issue without going shopping for something new