Time Machine: Enable encryption on a locally connected disk without deleting the existing content of said disk?
According to Apple's support documentation, you need to remove the disk and re-add it as an encrypted disk:


Choose Apple menu > System Preferences, then click Time Machine.
Click Select Disk or Add or Remove Backup Disk (if you have multiple backup disks).
Select your backup disk, then click Remove Disk.
Set up the disk again as an encrypted backup disk.