Moving edge nodes between vCenter via cross vCenter vMotion or re-register can cause issues. If you have already moved edges to the new vCenter and are getting alarms, please see VM moref id alarms after NSX Edge cross-vCenter vMotion.
To redeploy and Edge node, please refer to the online documentation Redeploy an NSX Edge Node.
Edge nodes do not need to be in the same vCenter as the segments they are serving as long as the same Transport Zone is configured in both environments.