Hey yckhor,
Welcome to the site. I sometimes fish under the northern side of the Harbour Bridge and although I don't usually catch anything of size, I don't believe there are any restrictions. Not sure about the southern side under the bridge.
If you plan on fishing the Harbour Bridge area, on the South West side you have the piers in Walsh Bay, a short walk away. I'm not sure what pier you can fish, but I think it's the one with the floating ferry wharf. From here you can catch Kingfish, Bream and Squid. On the North East side, there is Jeffery Street Wharf where I have caught Bream, Jewfish, Kingfish, Squid and the occasional Blue Swimmer Crab. Just be aware of the ferries which pass through there during the day, so I recommend fishing it during the night or early morning, but if you do decide to fish it during the day be very vigilant for ferries and pull your line in when they approach. On the North West side of the bridge the wharf near Luna Park can hold Arrow Head Squid during the night. Hope this information helps and I wish you luck in your fishing adventures.
Cheers,
FishingGuy