This answer is more of a general one, and it can be different for Hong-Kong. But generally, you are taking a huge risk but it is still permitted.
If you have only one ticket, then you should be totally fine. Airline will take care of your baggage if any, and if the first flight was delayed, they will compensate you and/or arrange alternative flights because. Note that it should be one ticket, and all flights should be under one PNR/E-Ticket number.
One World and such flight flight alliance can probably make things a little bit better (they take some responsibility if the flight was delayed, etc). Cathay Pacific (Hong-Kong based airline is in One World FYI). But again, this is not a really good point to ask the airline for alternative flights if your flight was delayed.
If you have separate tickets, then it becomes your responsibility if you no-show to the second flight. Given that you have only one hour, I would not do this if I was you. One hour is not enough time even for a domestic flight. Since it's the same terminal and you have no baggage, it's technically possible to do it, but once again, you are taking a big risk.
Make sure you have the boarding passes ready.
If you do not have boarding passes, or need to check-out/in baggage, then you have to go through security, immigration and customs. There can be a lot of crowd in the passport checking counters, and you will probably need to walk a lot to go to the security and come to departure area.