During emergencies pilots are authorised to dump fuel, but is there any way or method to recover the fuel that has been jettisoned?
In theory it could be done, you could rapidly dump fuel into empty tanks below the wings and drop them. At a certain height they deploy Parachutes and land. Just like the Space Shuttle ejects the side tanks.
Some fuel dumps are only authorized over water and it would cost more to rescue the tanks and bring them back to the airline.
Over land they'd probably smash into populated areas.
The cost for saving some thousands of $ of fuel is not fesable for the rescue.
Short answer yeah it could be possible, but dangerous and costly.
In practical terms, no. If you wanted to save/recover the dumped fuel then you would have only two basic options: dump the fuel as usual and then recover it somehow from the air; or, pump the fuel in a controlled way into a container outside the aircraft.
The first option is probably impossible: how could you capture a huge cloud of fuel and fuel vapor mixed with the air? That would be like gathering water from clouds.
The second is theoretically possible, but for civil aviation at least it probably requires too much equipment and risk. You could pump the fuel into a drop tank then jettison it with a parachute for a soft landing. Or you could pump the fuel into another aircraft via a tube, in a kind of reverse air-to-air refuelling. Or if you're dumping fuel from a helicopter (does that ever happen?) it could hover over a tank on the ground, pump out the fuel and then land.
But all of those suggestions are totally impractical (again, at least for civil aviation). Adding drop tanks or air-to-air hoses would add huge cost in materials and training and reduce the useful load of the aircraft significantly, all for a situation that rarely occurs. And for air-to-air pumping you would need an empty tanker aircraft to be available immediately, which is highly unlikely, plus there is the inherent danger of operating two aircraft very close together.
Since fuel dumping is an exceptional situation and many aircraft can't dump fuel anyway, it seems unlikely that investing in a recovery solution would be worthwhile.
By conserve you mean collect for later use I am assuming. While it is technically feasible to do that it is extremely impractical. You'd have to either have another aircraft fly in formation in some sort of reverse in-air refueling system, or the pilots would need to fly over a system on the ground which would collect the fuel.
Any system to do this would require precision on the part of the aircraft needing to dump fuel, and in the kind of emergency where dumping fuel is required precision is one thing you aren't likely to get. Also, the cost of implementing a collection system far outweighs the cost of the fuel you'd save.
I suppose the least expensive way to do it would be to reinforce the airplane structure so that it coud land at maximum takeoff weight. Then no dumping would ever need to occur.
Still not cheap enough to be practical, though. The weight of that extra structure would take fuel to carry around at all times, to save fuel only on the rare emergency.
The pilot can either keep circling around to burn it off (doesn't conserve it) or just land overweight without jettisoning.
Burning it off is not an option if you want to get on the ground now to deal with the emergency. And landing overweight can create a new emergency if the gear collapses/too many tires blow.