Serve web static pages stored in S3 bucket from Eks cluster

If you have created a static website on S3, you don't need a load balancer in front. Instead you can use Cloudfront as a CDN for your static website - https://docs.aws.amazon.com/AmazonS3/latest/userguide/website-hosting-cloudfront-walkthrough.html

If you have single page applications on your static website build using frameworks such as React.js or Vue.js, and you need to make dynamic API calls to your APIs running on EKS, then you can use a Kubernetes Ingress Controller for those APIs. That can be NGINX or you can use the AWS Application Load Balancer for your APIs - https://docs.aws.amazon.com/eks/latest/userguide/alb-ingress.html