At the outset I can tell you that this experience could have ended badly. Instead I was impressed with Nikon service. That needs to be said since I was set up for a bad experience by some old Internet posts concerning Nikon D750 shutter failures..
The problem began while we were on vacation when we visited both Salt Lake City and Yellowstone National Park in August 2019. For trips such as this I carry my Nikon D750 with a Nikkor 24-120mm f/4 kit lens. The combination is great for street photos as well as vacation photos where I sometimes like to shoot interiors with high ISO.
At some point the camera began displaying ERR on the LED when turned on. The message went away with the first press of the shutter. Later, that symptom was combined with another, an occasional black bar across the top of the image frame. The occasional black bar became a regular black bar across all frames. Finally, the message ERR was displayed and the camera would no longer operate.
There is a history of this failure early in the life of the D750 product. The D750 was released in September 2014. I purchased mine in April 2016. There was plenty of discussion about this on the Internet at the time. There was a recall and Nikon issued the second technical service advisory concerning the problem on 12 July 2017. I did not know about the service advisories.
I logged into the Nikon repair site and received an initial repair estimate of $282.95. I was disappointed that the camera was broken because I like it a lot and because I have several lenses for it that I also like. I rationalized that the cost was worth it. There was the risk that I was not going to be happy with the repair.
I boxed the camera body and sent it to the Nikon repair facility. I received a timely notification from Nikon that it had received the camera. The notification directed me to their web site to approve the repair.
When I got to the site and logged in with my repair number, I received a nice surprise. There was to be no charge for the repair. The exact scope of the repair was not noted.
Ten days after sending the camera to Nikon I received the repaired camera. The scope of the repair was detailed on the packing slip and it was significant. The shutter was replaced, the camera was re-calibrated, and it was cleaned. I tested it with a few quick shots and think that it operates as it did when it was new.
Time is needed to determine the quality and the longevity of the repair. I would be happy to get another three years of operation from the camera. The D750 remains an important camera for me when I need high performance and I am very happy that Nikon still honors their commitment to fix this problem.