score:3
There are two routes you can head down, which depends on if your backpack is a high-end or a low-end one.
High end backpack
If your backpack is one of the more-famous, branded ones, chances are that they will have a local distributor (代理商) in Hong Kong. You should contact them and see if they can get it repaired/replaced, though of course it will cost you some money. Alternatively, see below...
Low end backpack
It is very likely (if not almost certain) that you can find a tailor and needle-work shop (縫衫舖) hidden somewhere near you in Hong Kong. In urban area, they may be tucked away in a corner upstairs of a low-end shopping mall. In new towns, every housing estate that has some sort of shopping area is likely to have one.
These shops don't make you suits, but provide garment alteration, replace missing buttons, and sometimes sell you all the yarns and accessories if you want to knit yourself. In my experience (when I was young), they service a wide range of products, doesn't charge you a fortune, and it seems there are little they can't fix. However, expect some difficulty in verbal communication as it is likely the shopkeeper doesn't speak much English.
You didn't mention which neighbourhood you are active in Hong Kong, and hence I feel unable to tell you where exactly you should go (due to my limited knowledge once outside the neighbourhood I used to live in). However, if you flag someone who isn't in a rush down and ask (or show them):
Chinese: 附近有冇縫衫舖?
Cantonese pronunciation (non-standard): fu gun yau mo fung saam po?
English meaning: Are there any tailor/needle-work shops nearby?
...or even
Chinese: 我條背囊帶爛左,邊到可以整?
Cantonese pronunciation (non-standard): ngor teeu booi lawn daai laan jor, been dou hor yi jing?
English meaning: My backpack strap is broken, where can I get it fixed?
They should point you to the right shop.