There are two ways to do upgrading a KOPS cluster.

This is the 1st way to do.
1. list the KOPS cluster.
$ kops get cluster
2. edit the particular cluster and update the version.
$ kops edit cluster --name CLUSTER_NAME
Then change 'kubernetesVersion: x.xx.x' older version to 'kubernetesVersion: x.xx.x' new specific/particular OR latest version.
3. check the current version by using the commands.
$ kubectl version --short
Server Version: vx.xx.x                     # its current older version
$ kubectl get nodes
Nodes (Master & Worker) is in old version.
4. update the cluster.
$ kops update cluster --name CLUSTER_NAME --yes
5. rolling-update the cluster.
$ kops rolling-update cluster --name CLUSTER_NAME --yes
6. finally verify the cluster is updated OR not.
$ kubectl version --short
Server Version: vx.xx.x                     # now its new version
$ kubectl get nodes
Nodes (Master & Worker) is in new version.

This is the 2nd way to do.
1. upgrade the cluster.
$ kops upgrade cluster --name CLUSTER_NAME --yes
This command will verify the old and new version.
2. update the cluster.
$ kops update cluster --name CLUSTER_NAME --yes
3. rolling-update the cluster.
$ kops rolling-update cluster --name CLUSTER_NAME --yes
4. finally verify the cluster is updated OR not.
$ kubectl version --short
Server Version: vx.xx.x                     # now its new version
$ kubectl get nodes
Nodes (Master & Worker) is in new version.

# Link :- https://medium.com/avmconsulting-blog/upgrading-and-scaling-kubernetes-cluster-in-aws-6971b3936465
          https://kops.sigs.k8s.io/operations/updates_and_upgrades/
          https://devopsbuzz.com/kops-to-manage-kubernetes/
