By Ronald Grover , Jennifer Saba and Liana B. Baker LOS ANGELES/NEW YORK (Reuters) – Chase Carey, Twenty-First Century Fox’s president and chief operating officer, may be feeling pressure to stay in his job for several more years both from his boss, Rupert Murdoch, and from the company Murdoch is trying to buy, Time Warner Inc. As Murdoch mulls his next step following Time Warner’s rejection of his $80 billion offer, some Time Warner investors say they are concerned about who might succeed the 83-year-old chairman and chief executive. In particular, they’re not sure whether Murdoch’s sons, James, 41, and Lachlan, 42, are ready to manage the integration challenge. The 60-year-old New Yorker, who’s been working for Murdoch since 1988 and earned a reputation for a no-nonsense leadership style, signed a two-year contract with Fox in June that gives him the option to opt out after 18 months.