When going in reverse i hear a clunking noise from

A grinding noise suggests a bearing at fault or perhaps worn pads on the brake rotor.

However, the clunking noise you mention could also point to a problem with the drive shaft or differential.

The first thing you should do is to get under the vehicle and try twisting the propshaft back and forth. If there's any movement this points towards a worn universal joint on the propshaft. A worn universal joint can cause a clunking noise - particularly when pulling away. The vibration caused by a worn universal joint can also damage bearings in the differential and also to the splined ends of the axle shaft.

You're also going to have to remove the wheel from where the noise comes from and examine the end of the axle shaft/bearing.

The link below is of images of the rear axle:

land rover discovery rear axle Google Search

Fixing Suspension Clunks And Rattles - Popular Mechanics

www.popularmechanics.com/cars/how-to/a110/1272531/
Have your helper sit in the driver's seat, turn the key to unlock the column, then rock the ... Older rear-wheel-drive vehicles with a live rear axle and coil springs may have what's ... The rod's bushings are a likely source of a clunking noise.

It's best to get a repair manual from an auto parts store. It will give you step by step instructions with diagrams. You'll need a large compliment of tools to do the job as well as a floor jack and jack stands of sufficient strength to safely support the weight of the vehicle.

find a mech with an electronic stethoscope.
$50 tool/
we can find any noise. source with this
except U-joints. on main drive shafts.

find a pro mech, they all know this.
Id put in new U-joints if , all my electronic hear tests pass/
see that logic?
i check axle ends, and pinion front bearing.
and engine , and tranny front center and rear.
all normal.> then U-joints are bad.

most guys just put them in , to start. can save time.
warning, all tests here are dangerous. that is why use
my remote monitoring stethoscope with zero risk .
person 1 drives, i rind shot gun and with head phones on
i stop and move my microphone clamps
takes about 30min to 1hr to finish a test.
my last catch, was a bad right axle bearing, RR.
i caught it early.
sounds can telegraph, so lots or listen points, prove who is the offender.

be looking u8nder the vehicle at the rear drive axles see if one of the cv joints is possibly broken..if the vehicle is off the ground on a lift..you can rotate the wheels and see the broken axle..

I seen this before and is the upper rear axle support, or the engine support just open your hood and see if the motor move to much, or get on the back the car and look under to see it the axle move to much wile some one is shifting. MAKE SURE TO APPLY EMERGENCY BREAK

Try changing the gear oil in the rear axle. Be sure to add a Slip Differential Additive paste to it (Autozone sells the paste and the gear oil).
The noise is coming from the differential in the rear axle and you will hear it when the vehicle changes from one direction to the other. Drive a hard zigzag line in a vacated parking lot and you should hear it at each shift in direction.

Change the front axle gear oil also if it had never been down. Usual interval for both is 30,000 miles.

this problem is an easy fix. your local part store(oriellys) can test the starter,alternator and batterie withouth you having to take them out of the car.

I can almost guarantee you it's not serious. Just u-joints.

Your front "ball & socket" joints are in dire need of lubrication. You need to do this:
Take the tires off, and look for a fill plug behind the hub, on the housing, above the ball & socket. Remove the plug, and fill it up with 80-90 gear oil. Replace the plug, do the other side.
What you have is a dry joint, and the clicking noise is coming from the u-joint (actually called a "Rzeppa" joint), inside the ball/socket/hub...a good lubrication will eliminate your condition. Hope this answers your question, please feel free to comment back with any other questions...And, thanks for choosing FixYa.