Have you formatted the drive upfront or did you just unplug it from the other computer and are attempting to use it directly?
One way of taking ownership of the individual partitions is to open the "Disks" program, select the external drive and partition you want to update, and the on the "additional partition settings" button choose the option "Take Ownership".
You'll see a prompt warning you about the operation. It should be fine to accept if you are not doing anything special with it, but take a minute to read and understand it.
By the way, please update your profile to specify which version of ZorinOS you're using: