You can keep the Gmail account and start using a new one somewhere else. You start registering to new services with your new account and gradually migrate old services to it if they let you. You end up with gmail for social logins (which hopefully you can migrate too) and little else.
I do have a Gmail account. I use it to login in Google when I work for a customer which use the Google Cloud, when I have to upload videos to YouTube (I logout after that) and for Google Play.