Creating a directory for your NEWSTORE and uploading ZC137 into it should not be a problem; the only problem you may have is whether your hosting package allows you to have more than one database (now you CAN run it from the same database using a different table prefix, but my own preference is to always keep development stuff well separated from live stuff - even more so if you're not 100% confident in what you're doing )

If your host does not permit this, now may be the time to consider switching to a Zen Cart Certified Host (who will be able to help if you have issues), and perhaps build your new store on there.

Whichever, there is no conflict between versions if you keep things apart.