The Magicians' Guild by Trudi Canavan is the first book in The Black Magician Trilogy and is about The Magicians Of Imardin, whilst cloaked in the protection of their sorcery roaming the streets to purge the city of undesirables, they have no fear of reciprocations from those they are trying to evict until one girl enraged, throws a stone at them and effortlessly bypasses their magical shield.
What The Magicians' Guild had long dreaded came to pass: someone outside their ranks possesses a raw power beyond imagining, an untrained mage who must be found and schooled before she destroys herself and her city with a force she cannot yet control.
When I first found this book by Trudi Canavan it was in the form of an audiobook (not from Amazon), unfortunately halfway through the audiobook vanished from my device, so I eventually read this book (some time later, after much searching) as a paperback edition. It was well worth the wait!
Available at Amazon.com & Amazon.co.uk.