DNS settings on the Non Primary NICs are not retained after Guest OS Customization even when the DNS servers are set up directly on External Network.
Cloud Director
By design, the DNS servers are only configured to primary NIC. All the DNS settings on non-primary NICs are cleared after guest customization.
This is an expected behavior. The reason is that the primary NIC is the main interface for the system's network traffic. Therefore, DNS configuration is applied to the primary NIC and cleared from the non-primary NIC.
To workaround this issue you can use a customization script to modify the guest operating system of the virtual machine, in this case to set the desired DNS configuration post customization.
For more information on creating customization scripts and applying them to a virtual machine see the Cloud Director documentation, Edit Virtual Machine Properties in the VMware Cloud Director Tenant Portal - Change the Guest OS Customization of a Virtual Machine.
https://docs.vmware.com/en/VMware-Cloud-Director/10.5/VMware-Cloud-Director-Tenant-Guide/GUID-FA8C101E-241E-41A5-A3C3-83BDBB4467F1.html#GUID-2B7A04E8-7479-4EE9-99B0-1A46751BE46F__GUID-658C5607-04BA-4BE1-87D3-8553DD2601EE