Further segmenting the existing system probably means a huge amount of changes to the existing system — more expensive than replacing the whole lot.
The old system will be based on detecting trains in "blocks", sections of track insulated from each other where the train's wheels make the circuit. I was about to say this would use relays, but Wikipedia says the first all-relay system was installed in 1929. So it's at least partly mechanical (levers moving in the way of other levers). The logic implemented in this will prevent the signalman from sending trains on a collision path, but only if drivers obey all red lights.
The new system will either be something similar, except implemented in electronics and stopping the train if the driver doesn't. But for a metro system, in order to get higher capacity, it will probably do away with the "blocks" altogether, instead ensuring that every train has a safe distance ahead of it. Maybe they will also automate the trains, so the train drives itself.
Either way, they'll probably upgrade the trains to support the new system, then install the new system in whatever sections allow it, then remove the old system once the new system is working correctly. I'd expect there's a huge amount of sunk cost once the project starts (design, modifications to trains, staff training etc) so it doesn't make any sense to stop halfway and keep the costs of both systems.
https://en.wikipedia.org/wiki/Interlocking