You can't merge Apple IDs. If you want to use the email address from 2013 on a new Apple ID, you will have to change the email address of the 2013 Apple ID to free up the email address to use with the new Apple ID.
First change the email address of the 2013 Apple ID. Note the restrictions in the article.
Apple ID Name Change. *
Make sure you turn off Find My Phone before signing out of the old ID. Once signed out and Find My Phone is off, then sign in with the new ID, then turn Find My Phone back on.
What to do after you change your Apple ID or password - Apple Support * I suggest doing this before you change your Apple ID or password.
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.
After 30 days, try using the 2013 email address with the new Apple ID
You can try setting up Family Sharing between the IDs if you want to be able to share purchases made with the IDs.
Family Sharing. *
ASC YouTube for Family Sharing
Family Sharing - Set up. *
Family Sharing - Set up on iPhone. -
Family Sharing - Set up Family Sharing in the Apple TV app. -