Try remembering the password you used with your defunct email and see if it gets you to your account.
If you can’t remember the Publons password, please get in touch with your email provider to try and regain access. Most of the email providers have procedures to restore access to accounts.
If logged in - add your active email address and verify it, so that you can use it to reset the password in future. It is a good idea to have multiple sign in options (verified emails, Google, Linkedin, ORCiD) added to your profile for the ease of use and to reduce the chances of losing access in the future.
We take your data security seriously so if you don't have access to any of the account's email addresses or connected accounts (Google, Linkedin, ORCiD), we are unable to regain access to that profile. While we understand that it can be disappointing, we use these verification requirements to make sure we don't give out any user information to the wrong person. Such accounts may be deactivated in certain cases, please create a support ticket for assistance here: https://publons.freshdesk.com/support/tickets/new