To protect online accounts from being accessed through a compromised email address:

1. Set up 2-factor authentication.
2. Set up two-step verification for services if it is available.
3. Choose a unique, complex and difficult-to-guess password.
4. Change the password periodically.
5. Set up a unique security question for each account.
6. Do not use the same password across multiple sites.
7. Do not open suspicious links or email attachments
8. Keep an eye on account activities.
9. Do not share the passwords with anyone.