Static IPs in Fargate

No, it is not currently possible to add a static IP or Elastic IP address directly to a Fargate task. However, you can first create a Fargate Service with a Network Load Balancer, and then attach the Elastic IP address of the task to the Load Balancer.

You can find more details about this process here: https://repost.aws/knowledge-center/ecs-fargate-static-elastic-ip-address