How can I remount an NFS volume on Red Hat Linux?

If your mounted points are permanent- placed in /etc/fstab - you can run mount -a to re-read fstab, which is same as a refresh.

You could also use remount in case of a temporary mount

It sounds like you need to change the ownership of the files -- not remount the share. The files will continue to be owned by the old UID since nothing has been done about that.

As root or with sudo: find /path/to/share/. -uid $OLDUID -exec chown $USER {} \;

That said, to answer the question you can remount a share on any Linux system with the remount option to the mount command.

mount -o remount /mountpoint