Encrypt Time Machine backups without deleting old backups?
Try at your own risk, but this might work:


Rename the {machine}.sparsebundle to {machine}-unencrypted.sparsebundle
Show package contents on the sparsebundle
Make a backup of com.apple.TimeMachine.MachineID.plist


Copy it to com.apple.TimeMachine.MachineID.plist.original

Open com.apple.TimeMachine.MachineID.plist
Set some placeholder value in com.apple-backup.HostUUID, for example seedotoriginal
Save and close


This should allow you to start making a new encrypted backup. Eventually {machine}.sparsebundle should appear next to the previous one ({machine}-unencrypted.sparsebundle).

If you need to restore from the unencrypted backup, you can replace com.apple.TimeMachine.MachineID.plist with com.apple.TimeMachine.MachineID.plist.original.

Once the encrypted backup procedure has completed, you can delete the unencrypted backup sparsebundle (watch out, that may take quite long).

Note that it might be still possible to fetch the deleted, unencrypted data from the disk. I would recommend getting another disk so that you can properly clean the disk from unencrypted files by writing zeros to it a couple of times, before starting to make encrypted backups on it.