Each service disconnecting means in separate enclosures must connect to the grounding electrode system.
There is more then one way to do it, but you generally either run separate GEC's to each service enclosure, or run a common GEC sized for all the enclosures and make taps to it from each enclosure.
Only one GEC is required and depending on what electrodes are available you run it to building steel or water pipe and connect all other electrodes to it via "bonding jumpers" or the jumpers can run from one electrode to another as well.