How could I make Cloud Run communicate with a kubernetes cluster?

I deployed an image on Cloud Run where I need to make http calls to a service that is inside a Kubernetes cluster.

This service can be only accessed from a private network.

I read on that article that I need to connect the cloud run instance to my private VPC, then I need to create a load balancer that will be mapped to one of my k8s service. That will get me a external ip that will not change and I could use in Cloud Run.

Did I understand it right ?

Then, how could I assign a hostname to that external ip ? I would need to update the dns that cloud run uses I guess ?

Answered by @Gari Singh, post this answer to help other communities to serverfault

Assuming you are using Cloud Run and GKE, you'd need to take the following steps:

Create a Serverless VPC connector to connect Cloud Run to the VPC where your GKE cluster is deployed:

gcloud services enable vpcaccess.googleapis.com
    gcloud compute networks vpc-access connectors create $CONNECTOR_NAME \
    --network $VPC_NETWORK \
    --region $REGION \
    --range $IP_RANGE

Reserve a static internal IP address:

gcloud compute addresses create $ADDRESS_NAME \
    --region $REGION --subnet $SUBNETWORK

Create a LoadBalancer for your GKE service and assign the static IP:

gcloud compute addresses describe $ADDRESS_NAME --region $REGION

The above command will show you the static IP you created

Create a load balancer service:

apiVersion: v1
kind: Service
metadata:
  name: helloweb
  annotations:
    networking.gke.io/load-balancer-type: "Internal"
  labels:
    app: hello
spec:
  selector:
    app: hello
    tier: web
  ports:
  - port: 80
    targetPort: 8080
  type: LoadBalancer
  loadBalancerIP: "YOUR.IP.ADDRESS.HERE"

You can use the IP address directly from Cloud Run, but you could also create a DNS name using Cloud DNS as well.