Also, for my brave Saturday Slash volunteers I will gladly do follow-up slashes (each more kindly than the next) on your query if you post them on the Query Critique board over on AgentQuery Connect. You'll get advice from me, and also people who are smarter than me. If you do post on AQ, be sure to follow the guidelines and let me know you posted so that I can follow up!
Breaking into a high security space station and getting out with anything but cuffs on your wrists is impossible for most 26th century thieves, but Jez Starwisp isn’t your average criminal. Nice hook. I'd consider starting a new sentence at "but," even though I'm sure somewhere along the way somebody probably told you that's a no-no. It'll reduce the run-on feel, and honestly, I think starting with "But" is perfectly fine. Raised on a backwards colony where the most advanced tech was a butter churn, she knows her way around lock picks and other archaic tools that top of the line security isn’t designed to handle. Along with her annoying android partner, Jez sets out to make a name for herself as the greatest thief in the Stymphalian solar system. Very, very good. Lots of voice here. You totally have my attention.
Her next target: Stymphalian Station Beta and a priceless statue belonging missing "to?" an important delegate. Everything goes according to plan, until the delegate echo here with "delegate," how about "owner" instead? enters the vault as she’s robbing it. Before he can raise an alarm, a security guard walks in and shoots the delegate another echo, how about just a pronoun here?, leaving Jez alive and well to take the blame. With a murder charge on her head, half the solar system is after her (not quite the infamy she wanted), and Jez is staring at the very real possibility of being sentenced to life on the inescapable prison planet. With the help of a bitter adversary, unscrupulous space pirates, and some old-fashioned skill, Jez has to clear her name, stop a murderer, and, oh, save a planet.
The Stymphalian system asked for a hero. They got a thief. Fantastic sinker.
The actual query that you've written here is very nice, but I'm fuzzy on two points. It could just be me, but I was under the impression as I read that Jez was captured (maybe it was the phrase "take the blame"), but it seems from subsequent sentences that she's actually on the run. So there needs to be some clarification there.
The other thing not quite working for me is the rather grandiose statement that Jez has to save the planet... um, where did that come in? I pieced together for myself that "stop a murderer" applies to the security guard (who presumably disappeared?) and therefore that makes me think there's some kind of political espionage at work here, which leads to her clearing her name and saving the planet. But I shouldn't have to put all that together myself (and I could be wrong, too).
Be a little more straightforward with your plot elements and you're looking good. Right now you've got a wonderful hook, and sinker, plus fantastic voice in the query. Honestly you've got the hard work behind you! Good luck!