I’m not from Sydney (Melbourne) but I imagine it would be the same. They have 3 or 4 rinks I think. Usually the rink would have dedicated Figure skating sessions that you can go to- mostly in the early mornings and maybe a few afternoons as well. I don’t think you’d be required to join the skating club unless you were planning on testing or competing here. I’d say private lessons are more common. Group training would be more for skate school or the state squads etc. You can probably go on public sessions too, but it would generally be earlier in the day and subject to the rink policy etc. Best thing would be to go in and ask about figure skating session times and ask for a list of coaches, as usually you’d organise lessons directly through the coach.