Delete Your Gmail Account
To cancel a Gmail account and delete the associated Gmail address:
What Happens to Emails in the Deleted Gmail Account?
The messages will be deleted permanently. You can no longer access them in Gmail.
If you downloaded a copy, either using Google Takeout or using an email program, you can still use these messages, of course.
NOTE: If you used IMAP to access Gmail in your email program, only messages copied to local folder will be kept; emails on the server and folders synchronized with the deleted Gmail account will be deleted.
What Happens to Emails Sent to My Deleted Gmail Address?
People who mail your old Gmail address will receive back a delivery failure message. You might want to announce a new or alternate old address to desired contacts.