Opportunities learning maths beyond the syllabus in HK
Hong Kong is filled with institutions that one can utilize to advance your learning in mathematics. I’m going to share a list of opportunities pursuing mathematics that I’m aware of.
Courses

CUHK EPYMT / SAYT
Enrichment Programme for Young Mathematics Talents are a series of courses that imitates learning mathematics at a university setting over the summer. There are courses suitable for form 36 students. Above all else, I recommend them the most as they give you the most authentic experience of what studying mathematics in university is like.

The dual programme provides secondary school students a very comprehensive learning pathway in the sciences. I have heard a lot of great things about the Dual Programme. In fact I wouldn’t be surprised if you could find friends in your secondary school that have participated in the programme before. Ask them what it’s like!

Hong Kong Academy for Gifted Education
Despite HKAGE being mainly focused in Olympiad mathematics training, it occasionally holds courses on other fields of mathematics as well. I’ve had very interesting courses on cryptography and quantum computing there, which are very far away from olympiad mathematics. Ask your mathematics teacher about how to join HKAGE through a School Nomination or through self nomination. After you’ve become a member you’d be able to join its courses.
Competitions

IMO Preliminary Selection Contest by HKAGE
If you would like to have a pathway of learning and competing in olympiad mathematics (even representing Hong Kong), the best way to do so is through the IMO Preliminary selection contest by HKAGE. All Gold, Silver, Bronze and Honourable Mention awardees are eligible for participating in the training sessions organised by HKAGE, which are very comprehensive. You can learn more about the contest

International Junior Science Olympiad by HKAGE

Hong Kong Physics Olympiad by HKAGE
These competitions, should you win an award and become eligible for training sessions, would once again lead you to a comprehensive training in the sciences. Even if you’re more interested in mathematics than physics, a good training in physics would be extremely helpful to your mathematical education. A lot of mathematical ideas throughout history are motivated by physics. You can find more details for these competitions here

Hong Kong Olympiad in Informatics (HKOI)
HKOI is an annual software programming competition. Once again should you win an award, it would lead you to a comprehensive training pathway. You could look at some of the training material that HKOI team members receive. A lot of mathematics is involved in competitive programming, such as graph theory, algorithms, computational complexity …

Other competitions
I would recommend focusing on competitions organised by HKAGE, as they are the only ones which leads to the most comprehensive training programmes / pathways for future learning.
However other competitions could be great fun! And it adds to your personal profile as well.
Mathematics societies
The value of mathematics societies comes from meeting and engaging with people. It’s through socialising with mathematicians that you become aware to new opportunities / pathways that you can take. You might even know older peers who have been through the same journey as you and could provide advice.

Hong Kong Joint School Mathematics Society
HKJSMS is a group of secondary school math enthusiasts. They mainly organise an olympiad mathematics competition every year. It’s a great opportunity to meet people interested in mathematics beyond your own secondary school.

Your secondary school’s mathematics society
If there isn’t one, start one! Get involved! You can ask alumni or even professors to give talks, organise mathematics discussion groups, start a mathematics journal, celebrate pi day … the opportunities are endless and you’d be amazed how helpful it could be to your mathematical journey.
Research Competitions

ST Yau High School Science Award
While doing research in secondary school sounds daunting, don’t be afraid of it! Just having the experience of looking up advanced mathematics on your own and writing mathematics is already extremely beneficial. HLMA recently has had a very strong social media presence on Instagram.
Others

If you’re interested into studying mathematics overseas in the UK, especially Oxbridge, you would find AAHK to be very helpful. It offers free one to one mentorship for oxbridge application to Hong Kong students, and does loads of talks / minicourses on what studying mathematics / sciences at a university level is like.
General Resources
There are obviously a lot of resources, especially online, on learning mathematics that is available to all
Here’s a few videos / books / websites that I’ve found especially helpful in no particular order: 3b1b Linear Algbera Series, 3b1b Calculus Series, STEP Support Foundation Modules; Oxford Online Maths Club, Numberphile Podcasts, 竟然成為數學家.
Oxford also releases pretty much all of it’s lecture notes and problem sheets online. It’d give you a good sense of what an undergraduate degree in mathematics entails.
In terms of online communities, Stack Exchange and Stack Overflow are great reads. The subreddit for maths is less serious / more for general discussions. There is also a Discord server for realtime discussions.