The second season, which doubles down on the intrigue and introduces a host of new characters, was just broadcast internationally. But it won't be available for viewing or streaming in Australia any time soon.
The first season of The Expanse was excellent -- you should watch it, if you haven't already. It's currently streaming on Netflix in Australia. It's marketed as a Netflix Original series in Australia, but it's actually produced and released in the US by SyFy
Australia's SyFy channel is run by Foxtel, and as far as we're aware there are no plans to broadcast The Expanse's second season on the pay TV network. More importantly, Netflix in Australia isn't releasing the show episode by episode -- again, as far as we're aware -- due to SyFy's hold on exclusivity until the end of the US season.
What's most likely is that we'll get the entire second season of The Expanse in Australia after the entire 13-episode run. With the first two episodes being broadcast back to back across the US a few hours ago, there are 12 more weeks to go -- so that's somewhere around the start of May.
We'll share a local release date -- whether that's on Netflix or anywhere else, and either for the entire series or episode by episode -- as soon as we have one. In the interim, can I suggest you take a look at Travelers to pass the time? [SyFy US]