Op,
I was up until very recently, in the same position as you. New role, hired on experience and merit. Started and the rot set in. I noticed it within a few days. Kept my mouth closed, bit my tongue. I happened to mention to my LM, that things appeared to orbit around her, was told, she is a huge help and had been a 'god send' following a takeover process where all the former team left. This colleague helped new owners through this tricky time.
As the weeks went on, I was professional at all times, but then started on her melt downs, asking my LM to meet her for a coffee whereby she hounded my LM about how I had taken over and she had been pushed out. My LM asked my advice about this conversation. I am in a job share now and my colleague who I share the role with, is fabulous, same level as me, same years of experience and so on.... I asked my LM to ask her opinion as I knew I wouldn't be able to give a balanced opinion as the hatred was now running deep.
My co-share had already seen the problem. She stated that as rhis woman had shone through a tricky time from the former team, this woman was able to shine through and LM became reliant on her. When I and my co-share started, her incompetencies became very visible. It was a very deep insight into the shape of her character.
I resolved to carry on. I went on annual leave. During my ten day absence this woman demanded to our owner that either I go or she did. Our owner is a hardened professional of many years experience. She showed her where the door was. Not because of me but that she would never be held over a barrel like that. So, another meltdown and she left without notice.
As PPs have said, if she was that good, she would have your role. She hasn't and there will be some reason for that. You have the role. My hater also applied for the role and clearly was smarting about that so set about making little comments to other people. Don't bend over backwards, always remain professional and if it gets too much, speak to someone. I wanted to give her my honest opinion but I knew I couldn't. My co-share always the consummate professional, had spotted it and remained tightlipped until she was asked.
Do not cut your nose off to spite your face. We can never alter the shape of a person's character, it can hide itself for a time, but eventually our natural traits present themselves. Stick it out for the FTC period. I am always on the side of seeing crap like this through until I could no longer tolerate it and examined why such a thing might occur in being disliked intensely. What did she see in me that made her dislike me. I saw it early on. My LM didn't until it was in her face. It is quite the exercise unravelling it all.
Good luck.