BEIJING — After more than a year of frosty relations bordering on hostile, South Korea’s leader, Moon Jae-in, pledged a “new start” Thursday in his country’s dealings with China as he met with President Xi Jinping, a re-engagement that China hopes will lead to stepped-up diplomacy on disarming North Korea. The two leaders moved to repair ties that had soured over China’s anger at the deployment of a U.S.