The controversial prospect of extraditions from Hong Kong to mainland China has thrown fresh doubt on the city’s status as a global financial hub.

A bill that would allow alleged criminals to be extradited to China has sparked the biggest public unrest in years. Aside from the short-term disruption, some in Hong Kong say the bill poses legal risks for employees, who for now are protected by the autonomy Hong Kong enjoys under a framework with China dubbed “one country, two systems.”

“Once...