Perform the following to update the Kubernetes version for your cluster :
From the Console :
1. Open the Amazon EKS console at https://console.aws.amazon.com/eks/home#/clusters.
2. Choose the name of the Amazon EKS cluster to update and choose Update cluster version.
3. For Kubernetes version, select the version to update your cluster to and choose Update.
4. For Cluster name, enter the name of your cluster and choose Confirm.
5. The update takes several minutes to complete.

From the Command line :
1. Update your Amazon EKS cluster with the following AWS CLI command. Replace the example values with your own.

aws eks update-cluster-version –region –name –kubernetes-version

2. Monitor the status of your cluster update with the following command. Use the cluster name and update ID that the previous command returned. When a Successful status is displayed, the update is complete. The update takes several minutes to complete.
aws eks describe-update –region –name –update-id

References:
https://docs.aws.amazon.com/eks/latest/userguide/update-cluster.html