If you really changed your Apple ID you won't have a problem. Also, if you really changed your Apple ID, there is no old one for you to delete.
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On the other hand, if you created a new Apple ID, see How to create a new Apple ID https://support.apple.com/en-us/HT204316. See the data implications below.
Some of these things may apply even though not changing an Apple ID: What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071
Keep in mind that some things available under a first Apple ID will not be available under a new Apple ID. For example, you won’t be able to transfer anything purchased from the App and iTunes Stores to the new ID. And, there are other issues to be addressed.
And see what Eric Root says on this matter here https://discussions.apple.com/thread/251343949 and
what Winston Churchill says about it here: https://discussions.apple.com/thread/7452747