I had a hydraulic noise develop from power steering. When I took off the reservoir cap, you could see bubbles streaming through the fluid when running. I have owned the XF since 8k miles, and it has never been serviced. The car now has 23k miles, so still it is not like it is old fluid. I put a vacuum pump on the reservoir to draw the air out of the system, and waited for 15 minutes, removed vacuum, and repeated. The bubbles and noise would reappear.
At this point I suspected that changing the fluid would be the next step. In the owner's manual, Jaguar calls for Mobil ATF 320. This did not seem to be readily available in US, not on Ebay nor Amazon. I called the dealer, who said he had 5 quarts on his shelf under the Jaguar part number, at $35/quart.
I then removed the fluid in the reservoir, added new fluid. Start engine, stop immediately, and remove and refill reservoir again.
Problem fixed! Quite as ever.
I will note that some forums say that Dexron is compatible, which it may be, but the viscosity and color of the Mobil ATF 320 is thicker and darker. The rack and pinion is made by ZF, and prior to looking it up in the manual, I suspected that they might have used Pentosin. Mobil ATF320 is definitely the original fluid, and I am happy that this is resolved.
Wanted to share this journey in case that anyone else encounters the same symptom. Hope this helps!

 

From the Jag dealer.

Note the lighter color of fluid that has stratified to the top. Not sure what this is.

I was surprised to see a type of a slime on the inside of the reservoir once drained. I would have thought that the high number of detergents in the fluid would have kept them in suspension.

This is the second extraction of fluid from the reservoir. It contains some new fluid mixed with old. The lighter color at the top is a lot less visible.

 

FWIW, our former 2009 XF had developed a very slight, but noticeable to me, "whining" noise, that would make itself known when turning in tight quarters. I had changed the fluid a couple of times in the past, using regular, synthetic ATF. This time, before pushing the panic button, Iwent to my local JLR dealer's parts department, where I discussed the situation. They informed me that JLR had brought out an "improved" fluid for the P/S units.

They sold me a couple of quarts of p/n STC50519, power steering and self levelling suspension fluid. I sucked out the old fluid the best I could, and topped the reservoir with the new fluid. I then drove out into the street, driving back and forth, while turning a couple of "figure 8s". Came back into the garage, sucked out the fluid, re-filled, and drove a few more "figure 8s". Repeated this 2-3 more times.....noise gone.

 

Thanks leadfoot4 for your reply! Here is the part number I got first, but was surprised when the jug was actually Mobil 320:
https://www.ebay.com/itm/Genuine-Jag...wAAOSw0wte~P0j

 

Just for grins, what color is the Mobil fluid? The oil that I got from the dealer was green.

 

Leadfoot4, it is a dark red as shown in the photo. Much darker and much thicker than Dexron. Hope this helps.