how can I reuse my old email address for my apple ID

No. If that email address is still associated with an AppleID that you've forgotten the password for, you would need to reset the password to regain access to that AppleID. But you cannot make a new AppleID with that address if it is associated with an AppleID.

If you deleted the AppleID you used that email address to make, then you can never again use that address to make a new AppleID. See -> How to delete your Apple ID account - Apple Support

"Can I use the primary email address for my deleted Apple ID account to create a new Apple ID or with another existing Apple ID account?

No, once your Apple ID is deleted, you can't use the email address that you used with it to create a new Apple ID. In addition, you can't use that email address with another existing Apple ID except as a rescue email. Also, if your primary Apple ID email address is with a Custom Email Domain, it can never be reused to create an Apple ID after your Apple ID is deleted, even if the domain ownership changes."

You can change the email address on that Apple ID which will free up the address you want to use to be used with another Apple ID.

Apple ID Name Change.  * 

Apple hasn’t published any guidance for using an address again. Normally, if your e-mail address was associated with an ID in any way, for example as a Notification email address or a Rescue e-mail address, then it can't be reused as an  Apple ID email address for approximately one year. I have also seen posts that stated Apple told them there was a 30 day waiting period before the address could be used again. You will need to get another e-mail address from somewhere like AOL or Yahoo to use as your Apple ID or you can try waiting 30 days to see if that works.