If you can trying configuring the dns options for the docker image. Either of these two options have worked for DNS/VPN issues I've experienced in the past:

• --dns=<IP_ADDRESS>
• --dns-search=<DOMAIN>

Here's more detailed docs

One of the solutions is to create a service that will get a DNS response and route you to the external endpoint that is your database.

Steps:

• Create a service without selector
• Create an endpoint manually
• Test it

Create a service without selector

Create a service without selector by following this: link.

apiVersion: v1
kind: Service
metadata:
  name: DB_NAME
spec:
  ports:
    - protocol: TCP
      port: DB_PORT
      targetPort: DB_PORT

Replace the DB_NAME and DB_PORT with appropriate to your case.

Apply it by running below command:

$ kubectl apply -f FILE_NAME.yaml

Create an endpoint

Service created earlier will not have an endpoint to direct traffic to.

Endpoint below will be used when calling the service name.

apiVersion: v1
kind: Endpoints
metadata:
  name: DB_NAME
subsets:
  - addresses:
      - ip: DB_IP_ADDRESS
    ports:
      - port: DB_PORT

Make sure that the name of the endpoint is the same as used in a service above.

subsets:
  - addresses:
      - ip: DB_IP_ADDRESS
    ports:
      - port: DB_PORT

Take a specific look at above part and replace DB_IP_ADDRESS and DB_PORT.

Apply it by running below command:

$ kubectl apply -f FILE_NAME.yaml

Test it

Run example pod with curl installed and check if created service responds to your requests:

$ curl DB_NAME:DB_PORT

Alternatives

Take a look at additional resources which are explaining other paths:

• Kubernetes.io: Services without selectors
• Kubernetes.io: Pods dns policy
• Kubernetes.io: Add entries to pod etc hosts with host aliases
• Kubernetes.io: Configuration of stub domain and upstream nameserver using coredns