Transfer old Apple ID data to a new Apple ID on a new phone

If you want to use the same apps on the new phone, you'll have to use the old Apple ID, or create a new Apple ID for your existing account before.

Then restore from an encrypted backup you made in iTunes.

Change your Apple ID - Apple Support

About encrypted backups on your iPhone, iPad, or iPod touch - Apple Support

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. https://support.apple.com/en-us/HT201060

Family Sharing - Set up. https://support.apple.com/en-us/HT201088