We cannot know what that first contract said; I'd like to think employer was smart enough to include a provision to let you go if they didn't like what you were doing. Probationary periods aren't really relevant, and vaguely connect at times to state unemployment benefits eligibility.
Given an employer would be free to let you go regardless of an iron-clad one-year contract that gave them no "out" to decide they weren't happy with your performance, the best you could hope for in that scenario in a breach of contract action would be to go after seven months' worth of pay/whatever the contract provided for in compensation.
It's unclear unless you've got a very special skill set or are very high up in management/executive branch that they'd have a fixed-term contract with you in the first place vs. your employment being at-will.
"Do I have any options now that I have signed the new agreement?"
You can't really expect strangers to know the answer to this from here based merely on what you've posted. You may want to take the document to a local attorney for review.