How to route request to specific pod behind a service

I have a requirement to route requests to a specific pod in a replica set. The scenario is an HTTP client invokes a Kubernetes service SvcA. SvcA passes back in a header something like the host address of the pod or some other piece of information that can be used later by another client to access that same pod. The issue here is that I want to keep a database session open in SvcA with a local transaction already started. The connection/transaction will remain open until another client calls SvcA with the provided header. I need that second client call to end up on the same SvcA replica that the original request went to. Are there any out of the box solutions to do this? I know about Istio consistent hash, but it isn’t consistent across changes in the number of replicase.