If you've installed
gparted using a package manager, it has pulled any necessary X11 and GNOME libraries along with it as dependencies. You may need to install the
xauth package separately.
So, if you want to use
gparted GUI, you'll need to have a X11 server running on the system that has your physical display, keyboard and mouse, and then establish a SSH connection with X11 forwarding enabled. This will allow
gparted to send its GUI back along the SSH connection to your local system, where the X11 server will draw it onto your local display.
For Windows, VcXsrv is a reasonably up-to-date free X11 server software that is fairly easy to install. For use with SSH X11 forwarding, you don't typically have to configure it in any way: just make sure it's started before you start your SSH client, and make sure X11 forwarding has been enabled in your SSH client options.
The first time you establish a SSH connection with X11 forwarding, there should be a message like:
/usr/bin/xauth: file /root/.Xauthority does not exist
sshd at the remote host is using
xauth to prepare the connection, but since this is the first time, the
.Xauthority file in your home directory won't exist yet. This is normally just an informational message: the
xauth tool will automatically create the file if it does not exist.
In order to modify partitions using a X11 GUI tool, you'll need root permissions, so it will be simplest if you can log in directly as root. If that is not possible, you can log in as some other user, run
echo $DISPLAY to view the value of the
DISPLAY environment variable, then switch to root user and make sure the
DISPLAY variable is still set to the same value (re-set it if necessary). You will also need to set the
XAUTHORITYenvironment variable to point to the
.Xauthority file in your original home directory, i.e. something like