There is interesting GitHub repo which explain the use case plus how to achieve the static IP for fargate service.
Why?
A third party may want to whitelist your application's IP. Most of the steps are covered using-static-ip-addresses-for-application-load-balancers
Create Fargate cluster
Using the wizard create the cluster.
Along with the cluster it will create a VPC and Security group. Find
them and give them useful names.
In your security group for VPC set your inbound for HTTP and HTTPS.
Elastic IPs
Find it under EC2 > elastic IPs
Allocate two static IPs. One for each availability group.
Network Load Balancer
Find it under EC2 > Load Balancers
Create NLB. Under availability zones assign it the VPC and elastic IPs
you created earlier.
Create a new target group with target type IP and protocal TCP.
Leave IP blank. Next.
Application Load Balancer
Add existing security group from the VPC.
Create a new target group. Type IP. Protocol TCP.
Leave IP blank. Next.
Fargate service
Create a new service in your cluster.
Choose application load balancer you created.
Choose existing ALB target group.
The architecture diagram will less or more likely this
