In 2016, Mr. Xi put Mr. Luo in charge of cleaning up Shanxi Province, a northern coal-mining area plagued by corruption scandals. Mr. Luo oversaw a purge of the party’s senior ranks there, as a series of investigations documented broad misconduct.

Mr. Luo is an unexpected choice to run the Central Liaison Office because of his relatively advanced age, 65, and because he has already worked as a provincial-level leader in mainland China. He was also only a month into his latest job, in China’s national legislature, suggesting that the decision to send him to Hong Kong came together fast.

The Beijing leadership previously selected younger men with more expertise in the unique issues posed by Hong Kong, which has a different legal and economic system from mainland China because it was a British colony until its return in 1997 to Chinese sovereignty.

Like other Chinese provincial leaders, Mr. Luo has had some dealings with Hong Kong, especially over investment and business. He held talks with his predecessor, Mr. Wang, at least once, leading a delegation from Shanxi Province to Hong Kong in late 2018. On that visit, Mr. Luo also met the city’s chief executive, Carrie Lam, to discuss investment opportunities. But he appears to have no public record of ideas for ending the unrest in Hong Kong.

By contrast, Mr. Wang had spent most of his career as a Hong Kong specialist before he was named to run the office in Hong Kong in 2017.

When Mr. Luo stepped down as party chief in Shanxi, in November, he said he took pride in helping to clean up the province’s “political ecology” and overhaul its economy, two tasks that Mr. Xi may also want him to take on in Hong Kong. Mr. Luo also said then that he was most grateful to have the backing of Mr. Xi and other central leaders.

Mr. Wang and Mr. Luo are among the roughly 200 members of the Chinese Communist Party’s elite Central Committee, which gathers roughly once a year to discuss policy and review the performance of China’s political leadership.