How can I migrate my old and new apple id accounts?

No contents and no purchases and no subscriptions can be migrated.

Depending on the particular situation here, changing the associated email address (for instance) can preserve your access.

Here's the general sequence for resetting the email address:

https://apple.stackexchange.com/questions/197228/transferring-apple-id-purchases-to-another-apple-id

As for your own contents, download everything to your device or (for mail or such) transfer the contents to a different mail server, back up everything, disconnect, switch, upload what you can.

Here's what is probably a partial list of what would need to be transferred, if you are intent on migrating from one Apple ID to another:

https://discussions.apple.com/thread/8527161?answerId=33844690022#33844690022

https://discussions.apple.com/thread/7452747?answerId=29749666022#29749666022

Family Sharing can be useful in some cases here, but you're not able to migrate Apple purchases, subscriptions, apps, nor related history to a different Apple ID.