change which phone my iCloud plan covers

iCloud is not locked to a device, it’s locked to an individual’s Apple Account. If you are using the same Apple Account (formerly Apple ID) on the new phone you already have access to your iCloud subscription. If you decided to create a new Apple Account (not recommended) when you switched phones then you’ll need to cancel the iCloud subscription on the old phone and start a new subscription on the new phone. There is no transferring, it’s all about your Apple Account.

Downgrade or cancel your iCloud+ plan - Apple Support

You just need to sign the new phone into iCloud in Settings. If you had been using iCloud Photos, and you turn iCloud Photo on with the new Phone at Settings>[name]>iCloud>Photos, then all the pictures at iCloud will begin to fill your new phone.

If you don't want the old phone to be connected to iCloud, the you can go to Settings>[name]>Sign Out (at the bottom) to disconnect it from your account.