Our clubs here (in Sydney at least) are more like your sailing/ yacht clubs where racing is conducted, rather than businesses set up to hire out gear and provide lessons, especially for a bit more performance oriented stuff.

Maybe Balmoral Sailing Club as they have a sailing school attached, but even then it'll be Windsurfer LT's & longboards, not shortboards.

Your best bet is probably finding a kind soul to lend/rent you some gear for the duration of your stay...

After living here for over 15 years I can tell you that the windsurfing scene is nothing like that of Europe.

Not much in the way of clubs and the second hand market although is ok is no where as good as the uk, just not got the population here. This site and Facebook market place are the best places to look.

Also expect to travel to go anywhere. Gerroa which is two and a half hours south of Sydney gets a good wind in the summer.
Theres a few places in Sydney but not that many do instruction or hire, think Windsurf and Snow (WSS) might do something in Balmoral. Quite a few sail from Botany Bay as its fairly safe and doesn't get the ocean swell and Narabeen lake is good if you don't want to go ocean side.

I sail up Byron area which is a good 9.5 hours from Sydney, still in the same state.
If you are here for a while it would be better to buy second hand gear.

It is a different scene here to Europe. There is not so much in the way of equipment hire centres here. There are a number of clubs around Sydney that are involved with windsurfing, there are links to them here: www.windsurfingnsw.com/windsurfing-clubs/
It depends a little on what windsurfing discipline you are into. Some clubs have club equipment you may be able to hire, some run lessons and have coaching available. When you know where you are located, get in touch for some more specific advice.

There are a few options around Sydney.

The Georges River Sailing Club GRSC is south on Botany Bay near the airport. Offers irregular Sunday racing with a mixed fleet of iq, formula foil and wind wings. 2 to 20. No coaches but can be arranged. Dedicated parking.

Woollahra sailing club WSC at Rose Bay on
iconic Sydney Harbour is a popular club. Has regular iq sailors and coaching but not so much formal racing. 1-12 hour RESTRICTED parking.

Balmoral sailing club has regular Thursday afternoon racing with 0-5 iQ / formula foil sailors. Very difficult to park on weekends I hear. I think they have windsurfing coaches but maybe not foils.

Bayview sailing club BYRA on the south end of Pitt water is quite a way north of Sydney. Has a local iq member and offers some Sunday races. Not sure about coaching but good access to parking.

Marmong Point Sailing Club (MPSC) on Lake Macquarie is probably NSW's (if not Australia's ) best windsurfing club with races typically attracting 20 open foils fins and wings. No regular coaching and parking is ideal.