Follow the creatives whose work you've enjoyed in the past, a lot of them will post about stuff coming up or even just other stuff from friends and such that they'd recommend. Keep an eye on what's getting buzz around fringe festivals or other festivals of new works, even if you can't attend in person they'll usually release clips or songs to help get more traction.
Sometimes cabaret venues like 54 Below will have specific nights dedicated to young writers/new works and I've seen a couple performances that have made me want to keep up with them, and in those settings you might have a chance to speak with them afterwards to hear what's next for them.
Also just obsessively following broadway news from sources like BWW/Playbill etc. Broadway News does a daily newsletter where they'll often mention readings happening, granted a lot of these are NYC-centric.