Freeing up space · Recycle Vault
Why does a Recycle Vault item say it needs the drive to restore?
Short answer: That item's files are on your external drive, which isn't connected. Your Mac only keeps the list, so plug the drive in to restore it.
Because that item's files are kept on your external fast drive, and the drive isn't connected. Your Mac only holds the list of what's recoverable, so the window can still show the item — it just can't bring it back until the files are reachable.
Plug the drive in and restore as normal. Items removed while the drive was away are held on your Mac instead, so those can be restored straight away. See where the Recycle Vault is stored.