If you want to use the GUI to run the calculations directly, then I think the remote machine will have to run the Materials Studio gateway service and you'll have to make sure the ports are accessible through any firewalls in between your computer and the supercomputer.

Alternatively, you can write the CASTEP input files to disk and copy them to the supercomputer yourself. You then log into the supercomputer, queue up the calculations and, when they are completed, copy back any relevant output files to your own computer so Materials Studio can read them in and analyse them.