How do I recover the Apple Developer Account Holder role?

My organization’s account holder left the company. He used a private email address from his private domain when enrolling, so we don’t have how to take control of the email.

He is not denying transfer the account holder role to another employee, but he is taking a long time (more than a month now) to do that, which is weird.

Do we have another course of action?

The best course of action is to contact Apple directly and let them know the details of your situation. They should be able to transfer the account holder role, if they want. They would probably require a signed document from your CEO or similar.

I've gone through this before. The answer from jksoegaard is correct: you need to reach out to Apple Developer Support and request that the Account Holder (previously named Team Agent) role be transferred to a different Apple ID. The target Apple ID must satisfy all of the following criteria:

• Be a member of the developer organization.
• Have two-factor-authentication enabled.
• Be a named person, not a generic role; john.smith@my-org is okay. admin@my-org is not.

Additionally here are some good practices to follow on the Apple ID for your Account Holder:

• Use an email address issued and managed by the company.
• Make sure you can login at https://appleid.apple.com/#!&page=signin. This page has more stringent checks (prompting for security questions if they're set on the account) than logging into iCloud, for example.
• Associate two (or more) modern Apple devices with the account for routine access. I think the new iPod Touch is a perfect backup device for developers on a budget.
• Add two trusted phone numbers to the account for emergency access. Write a document that includes the full phone numbers and the people associated with them, then file it away somewhere safe. Apple won't tell you the numbers when you really want them.

  You should also consider verifying an additional phone number you can access, such as a home phone, or a number used by a family member or close friend. You can use this number if you temporarily can't access your primary number or your own devices.

And for anyone who ends up with the same problem I had -- an Account Holder that forgot answers to security questions -- don't bother trying to contact Apple to regain access to that account. They'll lead you in circles but never, ever help you regain access to it. Forgetting answers to the security questions means the account is burnt forever and cannot be recovered. Thankfully Apple is doing away with security questions.