I found myself in a similar situation a few years ago. After a widespread reshuffling of teams, I was put to to work with this person who was senior to me and came from another team closer to senior management. After a short while getting used to the new team structure, it became clear that this person was not easy to get on with, and I soon felt bullied and undermined at work. After putting up with it for a bit, I complained about their behaviour to my manager, and when he did nothing I elevated my complaint to his manager, citing specific examples of the kind of things that I felt were bullying. Some days later I was called to a meeting with the manager and this person, where they outright lied and denied my complaints. And at a later meeting with the same manager I was effectively demoted from my mid-level team lead position. It was not long after that, that I decided to look for a new job, before it got any worse.
Like with DJ's advice, maybe I should have gone to HR; maybe I should have kept detailed notes of the bullying rather than just what I could remember; maybe company policy or government legislation was there to protect me. But in the end you may have to admit defeat and look for a new job.