If I reinstall Elements, which is using an elicenser, would I need a new activation code?
I’m having trouble with some missing samples messages.
No. The activation code authorizes the license in eLicenser. Cubase (any version) doesn’t authorize anything directly. It simply asks the eLicenser if it is authorized to run on the computer and gets a yes or no back.
Adding this in case the OP does not know the difference between a Soft-eLicense and the USB-eLicense dongle or if it is being reinstalled on a different computer…
Regards 
Yes - it’s a soft license, not usb, and it would be on the same computer, not a different one.