How to Create Additional Google Play Account Under 1 Google Account?
You have a very strange use case, and Dan Hulme's duplicate suggestion is actually correct. 

If you want to use the apps from an OLD account, you need to add the OLD account, switch to the OLD account, and install the apps through the OLD account. Then, you switch back to the NEW account, and remove the OLD account. If you want to install a new app from the OLD account, you need to repeat the same procedure.

As I said, you have a very strange use case, and this is the only workaround. If what you wanted were possible, it would be open to abuse. You could share the account to several people, and let them install apps using that account.

EDIT #1: As per Izzy, removing the OLD account can break the installed apps, as the license checks will fail. So, best to keep both OLD and NEW accounts, but disable the sync on the OLD account (as you suggested).