As Beijing seeks to tighten its grip on Hong Kong, it has a new mandate for the territory’s powerful property tycoons: pour resources and influence into backing Beijing’s interests, and help solve a potentially destabilizing housing shortage. Chinese officials delivered the message in closed meetings this year amid broader efforts to bring the territory to heel under a National Security Law and make it more “patriotic,” three major developers and a Hong Kong government adviser familiar with the talks said. “The rules of the game have changed,” they were told, said a source close to Chinese officials, who declined to...