Short story involving ceramic pottery with a beautiful shine, and an inspector who is killed

Might this be The Potters of Firsk by Jack Vance? It was originally published in the May 1950 issue of Astounding Science Fiction magazine, and later reprinted in various collections.

Judging by this review from Goodreads, it seems to be a near-perfect match to your description:

"The Potters of Firsk" is a nineteen page short story that was published originally in 1950 in Astounding Science Fiction magazine. It is a very imaginative, creative story that demonstrates how early in his career Vance was able to produce well written, interesting stories.

The main character, Thomm, is asked about a beautiful bowl on his desk and tells the story of how he obtained it on the planet Firsk from fierce, secretive potters who used human bones in their glazes. These potters usually used the bones of the deceased per an ancient agreement with the local people. But "when the need is great, we do anticipate nature by a year or two...The soul lives forever in the pot it beautifies." One of Thomm's assignments on Firsk was to make sure that local people were not captured alive and used for their bones when the bone supply was low.

And having listened to this radio play of the story, I can confirm that

You can read a preview of the story here.