I have to wonder how you're going to run a ground ring just around the expansion. To qualify as a ground ring, it has to run around the entire building. EVen if you manage to do this just for the 'expansion', then the 'expansion' would have to qualify as a separate building and its GES would not qualify as the GES for the existing [separate] building...???
Also, providing the transformer is SDS, the GEC(s) is(are) run either to the transformer or system disconnecting means, wherever the system bonding jumper(s) is(are) located.