Hong Kong (CNN) On July 1, as Hong Kong marks 20 years of Chinese rule, the city gets a new leader.

Carrie Lam will be sworn in after she was selected by a Beijing-dominated committee in March to be the next Hong Kong Chief Executive.

Lam succeeds her former boss, CY Leung, who chose not to seek a second term and is leaving office with one of the lowest approval ratings of any Hong Kong leader.

Political reform

It is the "ultimate aim" of Hong Kong's mini-constitution, Basic Law, that the city's leader and the entirety of the legislature be elected "by universal suffrage."

Multiple attempts have been made to reform the current systems but limited progress has been made. In 2014, the Hong Kong government introduced a proposal that would allow all Hong Kongers to vote for the chief executive but only after prospective candidates won at least 50% support from a pro-Beijing body.

That proposal was one of the root causes of the 2014 Umbrella Movement -- which saw hundreds of thousands of protesters take to the streets -- and an attempt to pass it in LegCo ended in embarrassing farce as pro-Beijing lawmakers bungled a walkout allowing their pro-democracy colleagues to vote it down.

As deputy leader, Lam led the government's political reform efforts. "Like many people in Hong Kong, I of course want to see one person, one vote," she told CNN. "I tried very hard to deliver this ... but unfortunately it was not supported by some of the politicians."

Lam would not say whether her administration would pursue future political reform. In February , she warned that doing so might "draw Hong Kong into another series of divisions, and this is not favorable for the city's development."

Mathew Wong, an expert on Hong Kong politics at HKU, said the real decision lies with the central government and "Beijing has strong reservations about restarting reform."

"The last (effort) triggered the Umbrella Movement," Wong said. "In addition, Beijing has been insisting that the last reform proposal was a universal suffrage proposal, but the democrats turned it down."

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Article 23

Some warn the law could be used as an excuse to crack down on criticism of the government or discussing controversial topics like Hong Kong independence.

A previous attempt to implement Article 23 drew more than 500,000 people into the streets in 2003 and resulted in the proposed legislation being shelved and the minister responsible forced to resign.

More than 500,000 people took to the streets in 2003 to protest a proposed anti-subversion law.

Lam said critics were misguided, as all governments "need to protect their country and protect their countrymen" and in any case "freedom and human rights ... are also enshrined in Basic Law" and would therefore be protected.

She added that while this was a "constitutional responsibility," previous attempts showed her administration would first need to "create a condition" where passage of Article 23 could be supported, before introducing any bill.

Grenville Cross, a former Hong Kong director of public prosecutions, said that critics of Article 23 may be undermining themselves by forever blocking its passage.

"If Hong Kong doesn't enact these laws on its own then hardliners in the (Beijing government) might gain the upper hand and say ... we must take matters into our own hands," he said.

Photos: The top 10 most expensive housing markets 1. Hong Kong, China – For the seventh year in a row, the 13th Annual Demographia International Housing Affordability Survey: 2017 named Hong Kong the most expensive housing market. The survey uses the "median multiple" ratio system, which divides median house price by gross annual median household income. Hong Kong clocked a median multiple of 18.1, down from 19 last year. Hide Caption 1 of 10 Photos: The top 10 most expensive housing markets 2. Sydney, Australia – The second most expensive housing market for the second year running, Sydney has maintained a 12.2 median multiple -- the same as last year. For perspective, "severely unaffordable" housing is defined by Demographia as a market with a median multiple of 5.1 or higher. Hide Caption 2 of 10 Photos: The top 10 most expensive housing markets 3. Vancouver, Canada – Vancouver scored 11.8, making it the world's third most expensive housing market. Hide Caption 3 of 10 Photos: The top 10 most expensive housing markets 4. Auckland, New Zealand – Auckland is the fourth-least affordable market, while New Zealand is the second most expensive nation for housing overall. Hide Caption 4 of 10 Photos: The top 10 most expensive housing markets 5. San Jose, CA, US – San Jose, in Silicon Valley, has seen massive growth over the past decade. The housing market is currently among the most expensive in the US with a median multiple of 9.6. Hide Caption 5 of 10 Photos: The top 10 most expensive housing markets 6. Melbourne, Australia – With a 9.5 median multiple score, Melbourne has become increasingly unaffordable, pricing out many domestic investors. Hide Caption 6 of 10 Photos: The top 10 most expensive housing markets 7. Honolulu, HI, US – It might seem idyllic, but Honolulu is one of the most expensive markets in the world for housing. The island metropolis is the second least affordable in the US, with a median multiple of 9.4. Hide Caption 7 of 10 Photos: The top 10 most expensive housing markets 8. Los Angeles, CA, US – In Los Angeles -- which scored 9.3 -- housing prices rose the equivalent of 14 months in household income in only 12 months, the report said. Hide Caption 8 of 10 Photos: The top 10 most expensive housing markets 9. San Francisco, CA, US – San Francisco is among the most expensive cities in the US, with a median multiple of 9.2. Hide Caption 9 of 10 Photos: The top 10 most expensive housing markets 10. Bournemouth & Dorset, UK – About an hour southwest of London, Bournemouth and Dorset is the most expensive housing market in England. Hide Caption 10 of 10

Housing and inequality

Constitutional matters aside, Hong Kong is also facing severe problems of inequality, with a growing wealth gap and rising house prices that are increasingly out of reach for much of the city -- which is frequently ranked one of the most unaffordable in the world

The city's Gini coefficient -- an index from 0 to 1 that measures inequality, with higher scores indicating a more unequal society -- has risen from 0.525 in 2001 , to 0.539 in 2016 , the highest since records began almost five decades ago.

One particularly visible sign of inequality is Hong Kong's runaway housing market. The price per square foot has risen from around $450 in 2001, to more than $1,200 today, according to local property firm Midland Realty . This has resulted in absurd situations, such as a 161-square-foot apartment selling for around $500,000 despite being barely bigger than a parking space

Rents have also increased greatly , with Hong Kong tenants spending more and more money on less space.

Part of that increase has been driven by an influx of Chinese money, particularly in the luxury real estate market

Lam said she will work to "diversify Hong Kong's economy" in order to provide more opportunities for young people and "inject as much innovative thinking as possible" into the housing market.

She said she would introduce home ownership as a key policy objective of her government, "to try to let people to get a chance to own."

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Hong Kong's relationship with China

Underlying all these issues is Hong Kong's relationship with China. The city is governed by the principle of "one country, two systems," with a semi-autonomous government and limited political freedoms, but many have complained of growing Chinese encroachment

While her predecessor was criticized for not standing up to Beijing, Lam said her role was to act as a bridge between the city and the central government.

"I have to be honest, I have to tell the central authorities the feelings and sentiments of Hong Kong people, and if there are things I feel that we can handle, and they are totally in line with the provisions of the Basic Law, then Hong Kong should be given a free hand," she said.

As well as a rise in support for greater autonomy from China, or even full Hong Kong independence , there has also been a pronounced change in how people identify themselves, particularly among younger Hong Kongers.

According to HKUPOP , the number of 18- to 29-year-olds who broadly identify as Hong Kongers has risen from 58.3% to 93.7% between 2008 and 2017, while the number who identify primarily as Chinese has dropped from 41.2% to 3.1%.

Lam has expressed concern at this growing trend, calling for schools to teach children "I am Chinese" from age 3, but she also pointed out the two identities were not necessarily in conflict.

"The important thing is ... under 'one country, two systems,' we have full pride in being Chinese, and feeling proud of the progress made by the country," she said. "But at the same time, retaining as much as possible of Hong Kong's uniqueness and characteristics."