Sibling comment from thedrbrian explains it very well while it is unlikely to see clear air turbulence (CAT) with our current weather radars.
Of course if cost would be not an object we could detect these events. One possible solution would be to fly companion drones ahead of the jet. They could then detect CAT quite easily by just running into them. The spacing is critical with this scheme. If the probe drone is too far ahead you risk CAT developing between it and your plane. If it is too close you won't have enough warning time. If it is even closer you just rammed the drone and that can cause complications in itself.
Another possible option is to use laser backscatter. If you shine a laser forward from the airplane some of it bounces back from microparticles. If you measure the doppler shift of the light bounced back (probably with interferometry) you can tell the projected component of the relative speed of the particles. There is a ton of complications with this. But in theory you could make a "lidar" kind of thing which scans forward from the airplane and measure CATs directly.
The same kind which pushes the airplane? Heck you can just use two airplanes since we are talking about a situation where costs are not a problem. Everything else is just cost optimisation.
Of course if cost would be not an object we could detect these events. One possible solution would be to fly companion drones ahead of the jet. They could then detect CAT quite easily by just running into them. The spacing is critical with this scheme. If the probe drone is too far ahead you risk CAT developing between it and your plane. If it is too close you won't have enough warning time. If it is even closer you just rammed the drone and that can cause complications in itself.
Another possible option is to use laser backscatter. If you shine a laser forward from the airplane some of it bounces back from microparticles. If you measure the doppler shift of the light bounced back (probably with interferometry) you can tell the projected component of the relative speed of the particles. There is a ton of complications with this. But in theory you could make a "lidar" kind of thing which scans forward from the airplane and measure CATs directly.
Here is a paper from NASA about this possibility from 1968: https://core.ac.uk/download/pdf/80667132.pdf