Remove the graphical radar display completely. While in the old days pilots had all sorts of information, it for sure wasn't a graphical representation of that. Except for a printed or hand-drawn static map. Instead of the radar, add a radio channel that can be tuned to. There, an automated (but naturally sounding) aritifical intelligence will read radar reports. General ones when something of important is detected. And specific reports on request. With a bit of delay, until ground got a confirmation on the radar contacts.
In contrast to any graphical radar this works a lot more nicely with VR, because no additional screen is needed to constantly display the in-flight navigation computer to stay competetive.
This would probably provide much better immersion than anything that existed before, and add a nice challenge for the brain to process the audio reports.
edit: title Radio changed to Radar (obviously), and appended Radio
