Found this detailed and interesting answer by Alyssa Murphy (M.A. Art History, University of Pennsylvania (2013)) to the question, “What are some of the most interesting professions you can pursue after studying art history?” on Quora.
Some of the jobs that I considered pursuing with my art history MA: working for the FBI in art theft, ditto for the CIA. The IRS also works with art history academics in art-related tax matters (although that’s more of a side gig for professors, not something you apply for). Art law is a developing field that I personally find very interesting—specifically cases that involve repatriation or theft of art.
With many jobs, like conservation, or even curation, keep in mind that additional study beyond a BA or an MA (or even a Ph.D.) may be required. For instance, conservators are trained in chemistry and studio art (and it’s a very difficult field to break into). Many curation jobs, especially in the better museums, require a Ph.D.
In my experience, studying art history is a bit like studying English in that it gives you a broad understanding of history, culture, and the world and can be a good foundation for pretty much any career. Even doctors get training in art history to improve their bedside manner. I have an MA in art history but work at a psychiatry journal, but I still call on my graduate study practically every day.