Is this a Supplemental Ground or the Main/Primary GEC?
AFAIK, if you need to drive a second pipe electrode because the first one failed the 25 ohm test or because of local regulation, you can designate either one of them as Primary.
In the OP's case, it would seem to make the most sense (depending on the exact geometry involved) to call the original, already wired, one the Primary, call the second one the supplemental, and run a bonding jumper from the new electrode to the old one. If the new one is closer to the panel than the old one, then just running an additional GEC straight from the second electrode to the bonding point in the panel would seem easier.