I'm not really familiar with the iCloud Drive, sorry.
However, you need to be aware that:
- All purchases you made with your previous ID will be tied to that ID forever
- Contacts, calendars, bookmarks, mail messages, notes, shared photo albums, iCloud Photo Library beta, My Photo Stream are tied to the iCloud account, so wouldn't transfer to the new iCloud account with the exception of any that you told iCloud to keep on your Mac (or your Device) when signing out of the original account.
Did you intend to have a totally new, separate account? Because if all you were doing was changing the Apple ID email address, you can do that via Manage your Apple ID and continue to retain the same account.... Apple - My Apple ID
BTW - the original iCloud info will still be out there. If you want to, say, re-create your contacts on your new iCloud account, you can go to iCloud.com and open the Contacts so you have a point of reference.
So, if you did not select the "Keep on My Mac" option as you were signing out of that old account, you can always sign it off again and then sign back off and tell it to Keep whichever items it allows you to keep. Then, when you sign on your new account and turn on the various options for iCloud syncing, it should ask if you want to Merge the information for that option - select Merge to get that info pushed up to the new iCloud account.
Cheers,
GB