Model microservices
If you're using your model in a server side context and you're managing multiple models, you might choose to treat each individual model (or each individual model version) as a separate service, usually using some sort of packaging mechanism like a Docker container. Then that service is often made network accessible via some sort of service, either using JSON over HTTP or an RPC technology like gRPC. The key characteristic of this approach is that you're defining a service with a single endpoint that just calls your model. Then you do do all of your model management (promotion, rollback, etc.) via whatever system you already use to manage your services (e.g. kubernetes, ECS).
Model servers