Can I use an existing Ground Rod for Sub-Panel in Detached Garage (Meter box is using the rod currently)
You must tie to the existing grounding rod...
Since there's a rod present there already, you must tie your new subpanel's grounding electrode conductor to it, as per NEC 250.50 and the reference to Part III of Article 250 in NEC 250.30(A).
...and may be required to drive a second
If your existing rod is judged not to meet the 25ohm standard in NEC 250.53(A)(2), or if the AHJ wishes it, you may need to drive a second grounding rod 6-8' away (or more, if you wish) from the first.
You can either tie to the existing grounding electrode conductor with a 6AWG copper wire and an appropriate tap connector, or simply run the new rod's grounding electrode conductor back to the grounding bar on the subpanel, though.