How do I retrieve my old iTunes account?

1.

Depending on what you did with your 'old' Apple ID / iTunes account.

If you have deleted it, it is no longer valid, it simply no longer exists and it no longer works.

To understand about a deleted Apple ID, see the Apple articles below:

How to delete your Apple ID account

How to delete your Apple ID account – Apple Support (UK)

-> Once your account has been deleted, Apple can't reopen or reactivate your account or restore your data.

Understand and control the personal information that you store with Apple

Understand and control the personal information that you store with Apple - Apple Support

2.

If you've ever requested to deactivate your Apple ID, see -> How to deactivate your Apple ID account

How to deactivate your Apple ID account – Apple Support (UK)

⤵️

Scroll to ->  How to temporarily deactivate your Apple ID

Sign in to your Apple ID account page on a Mac, PC, iPhone, or iPad. Then scroll down to Data and Privacy, and select "Manage your Data and Privacy." On the following page, select "Get started" under "Deactivate your account." If you don’t see this option, it means that this feature is not available in your country or region. 

👉 When you request to deactivate your account, you receive a unique alphanumeric access code. Make sure that you keep this access code in a safe place—you must have it to reactivate your account. 

If you forgot the access code, try to contact Apple Support -> Get Support (apple.com)

3.

If you still know that 'old' Apple ID, check your Apple ID via your email box.

See this Apple article: If you forgot your Apple ID

If you forgot your Apple ID email address or phone number - Apple Support

OR see -> Having trouble signing in?

https://iforgot.apple.com/password/verify/appleid

Get support and assistance from Apple directly, see  -> Contact Apple for help with Apple ID account security

Contact Apple for help with Apple ID account security - Apple Support