The Strangler Pattern proposes a way to incrementally replace an older system with a newer one. You would put some sort of facade in front of the older system, which you will use to selectively forward requests to the newer system.
With this approach you would progressively migrate the existing functionality (and potentially new features) from the older system to the newer one. Opposed to a big rewrite, you would use the facade to route the requests to the newer system as it’s being built.