I am a little corn-fused by the description, but let me take a shot at this anyway...
Isn't the Grounded Conductor bonded to the Service Equipment + Grounding Electrode System, in either the UGPS or the Service Section already?
Seems like it should be, and the Grounding Electrode Conductor would be sized per 250.66, according to the Service Feeders' size.
You would need to effectively Bond the new Service to the UGPS, via a Bonding Jumper or suitable Bonding Fitings), but I do not think you need to create an additional GES, or add supplimentary Electrodes (Ground Rods) to an existing GES: -
*** unless there is nothing to suppliment an existing Cold Water Electrode ***,
then I could see a need to add an additional supplimental electrode.
What's funny (wierd funny, not "haa-haa" funny) is there will be unbalanced current flowing on the GRC between the new Meter Socket / Service Section, and the existing Service Equipment; due to the solid bonding of the Grounded Conductor to the enclosure of the new Service.
Let me know if this is / isn't applicable to your question.
Scott " 35 " Thompson
Just Say NO To Green Eggs And Ham!