Obernewtyn (The Obernewtyn Chronicles #1)
There was the time before, there was technology and now there's very little, in fact it's in the hands of some of the fanatical religious Council. There are people who are misfits in this world, people with psionic talents are punished and often killed. She is brought to Obernewtyn, where some evil people intend to use misfits for nefarious reasons.
Elspeth is a misfit and is trying hard to survive and now in Obernewtyn she finds herself with a destiny and a hope for her future.