For Cloud Director 10.5.1 and later follow the updated steps which include stopping and restarting the Cloud Director services as part of the process, Replace or Renew the VMware Cloud Director Appliance Management Certificates.
To resolve the issue in earlier versions of Cloud Director simply stop the Cloud Director services on the Cells before changing the Appliance Management certificate and start the Cloud Director services on the Cells after the new certificate has been applied.
Example steps would be as follows:
Backup Cloud Director before making any changes, Backup and Restore of VMware Cloud Director Appliance.
Stopping the Cloud Director services on the Cells will make Cloud Director unavailable so schedule maintenance for the change as appropriate.