The first step would be to remove all the red tape and artificial barriers restricting this airspace. It is ridiculous. Its like to kids arguing to their parents that the other is waving their hand in front of their face (I used to do that to my sister, hahaha....when I was 6

).
What should they do? I'm glad you asked, here is my opinion.
1. The first thing that needs to go is the stupid turn to final when coming in to the 7s. There is no reason we can't join final somewhere west of Macau. Final to 7L and R crosses MFM at least at 6000ft on a 3 degree slope. That is plenty of room for their departures and arrivals since final to HKG overflies the airport of Macau. This would allow ATC much more freedom in the spacing of aircraft to those runways. The same should be done with 25s, which they seem to do already when it is late at night.
2. More entrance and departure points in all directions. All transpacs should be allowed to leave on multiple airways that overfly the eastern part of China towards Xiamen. It is shorter and gives more freedom of choice in initial altitudes as they line up to cross the Pacific. This also includes north gates into china, without these ridiculous altitude restrictions that require climbs in HK airspace.
3. HK has to join the rest of the world in applying closer separation tolerances. That means not telling a guy to expedite TO when there is a guy on final to the same runway 10 miles out

(I could TO, fly a tight pattern, and then land and clear the runway in that time!) It also means using BOTH runways for TO and LDG. So what if you have to wait a few minutes before TO for arrival traffic. This is a complement, HK has a great system that rarely breaks down, I'm just saying we can take the training wheels off. Just as long as we keep the A-team working the tower or at least pay better to attract more professionals.
All these are dependant on China's government growing up. Here you have this country spending billions on infrastructure, building these amazing airport meghubs that aren't being used to capacity due to the archaic communist airspace by which they are surrounded. It is like building beutifull, wide highway on-ramps for a dirt road. There is no reason that China needs so much friggin restricted airspace over miles of nothingness. Me thinks it is time for them to evolve, so maybe things will change in a few hundred years.