These charts show how Hong Kong is faring as it clings to its zero-Covid strategy

Lam has insisted, however, that there are no plans for a "widespread city lockdown."

"As far as Hong Kong is concerned, we need to find our own way out of this epidemic, and so far, our measures to contain the spread of a disease remain a legitimate and valid one," she said.

This month, Lam said the city would stick with what it calls a "dynamic zero" strategy, at least until the vaccination rate hits 90%. The Hong Kong government describes its "dynamic zero" strategy as having a target of having "zero infections" — a strategy it has repeatedly said is the most effective way of fighting the pandemic. It entails measures such as mass community testing, sewage surveillance, contact tracing, and border controls to keep out imported cases.

But that 90% goal remains elusive as Hong Kong confronts relatively low vaccination rates, especially among the elderly.

As of Feb. 22, 59.84% of Hong Kong residents aged 60 and older had two doses of a Covid-19 vaccine, according to government data. That figure drops to 45.46% for those aged 70 and older.

Lam has said the city needs to "do better" in inoculating the elderly in order to hit the overall 90% vaccination rate target.

"Until all those things happen, we will continue to adhere to the current strategy of trying to contain the spread of the virus, or what we call maintaining this 'dynamic zero' regime," she said.

Hong Kong, alongside mainland China, is one of the last places still taking a zero-Covid approach. The city has maintained tight restrictions as it works toward establishing quarantine-free travel with China.

But the measures have hindered operations and snarled travel plans, according to a recent business sentiment survey conducted by the American Chamber of Commerce in Hong Kong.

In its annual report, HSBC said on Tuesday that "The evolving Covid-19 restrictions in Hong Kong, including travel, public gathering and social distancing restrictions, are impacting the Hong Kong economy, and may affect the ability to attract and retain staff."

Data from the city's immigration department shows the number of work visas issued has dropped over the last two years. Just 13,800 foreign professionals were issued work visas under the General Employment Policy scheme last year — a decline of about 66% from more than 41,000 in 2019, before the pandemic.

That decline, however, is likely only partly due to Covid restrictions, said Lloyd Chan, senior economist at research firm Oxford Economics.

"In addition to the travel curbs and US-China tensions, we think that concerns over the national security law and changes to Hong Kong's political system (such as the overhaul of the city's electoral system) have weakened Hong Kong's appeal to foreign companies and investors as an international hub," he wrote in a Feb. 9 report.

"Firms appear to be having difficulty recruiting overseas talent, as suggested by anecdotal evidence," he said.

InvestHK, Hong Kong's government agency for foreign direct investment, responded that Hong Kong remains "a major regional base" for businesses despite pandemic-related challenges.

"Hong Kong continues to offer overseas businesses unparalleled access to Mainland China markets, which is our biggest competitive advantage," InvestHK said in a written response to CNBC.

Hong Kong's banking sector is "as robust as ever" since the implementation of the National Security Law, the agency said. Total deposits in Hong Kong at the end of June 2021 were up almost 8% year-over-year to more than $15 trillion Hong Kong dollars ($1.92 trillion), the agency said.

A spokesman from Hong Kong's information services department told CNBC that the national security law has "reverted the chaotic situation ... restored stability and increased the confidence in Hong Kong, thereby allowing the city to ... return to the path of development."

The changes to the electoral system, meanwhile, ensured that members of the legislative council acted "in the interests of the country's development and the long-term prosperity and stability of Hong Kong," it said.

This week, authorities extended a ban on incoming flights from nine countries, including the United States, United Kingdom, India and Australia until April 20. The government has said the tighter border would "prevent imported COVID-19 cases from placing additional pressure on the city's healthcare system at this crucial juncture of curbing the local epidemic situation."

In order to reopen borders with China, Hong Kong has to align with Beijing's zero-Covid approach, Chan said.

"Thus, stringent international border restrictions will be maintained, hindering international connectivity and depressing inbound tourism. As a result, we anticipate Hong Kong's zero-Covid policy will hinder the economic recovery and weigh on its attractiveness as a global financial hub," he wrote in a Feb. 9 report.

Hong Kong's cumulative caseload remains low compared with other global cities, at just over 75,000 cases as of Feb. 22, according to government data. For much of the pandemic, daily new cases in the Chinese city were often in the single digits, if any.