"You may not recover missing jewelry from airliners, but the Montreal Convention stipulates airlines are liable for baggage theft. Report items to the airline within seven days for potential compensation up to 1600 USD. However, most airlines' policies instruct passengers not to put valuables in checked bags."
"You may claim: with the airline, though success varies; use baggage insurance; claim on home insurance (consider impacts on claim history/premiums). With enough funds, possibly hire a PI to locate the item."
"Reach out to the airport operator or local government, they may be able to assist in investigations. Try a Freedom of Information request for baggage video. Mention it to staff next time you fly, they might help too. Good luck."