Yuck. Just stay professional, over communicate projects to your boss, etc. your boss should have a better transition plan now that you're back. In my case, when I joined and 15 yr veteran wouldn't truly back off, a male colleague had to explain to her that for "work load purposes" we have more great people here. So you focus on your work and she will focus on her work, even if it got reallocated with the new hires.
Anyhow, she is still unnecessarily territorial and doesn't understand the definition of "coverage model". Boss won't clarify either, don't want to hurt feelings of the under qualified person who has been stuck in the same level for 10+ years!

So someone joined my department a few months ago. I went out on leave shortly after this person joined and now that I'm back things are weird. Weird like, to the point where other people are noticing and asking me what's up with our working relationship. This person talks over me, leaves me hanging and then tries to show me up, and implies they know more than I do about our organization. I think because I am younger and was more quickly promoted and there first, this person is trying to overcompensate. I have a closer relationship with our boss and I am confident our boss respects and values me. It is a very small department and we are peers in title, however I have more direct/recent experience. This person has two decades of professional experience in a related but not exactly identical field, and is used to having a team to manage. We have relatively high profile and high visibility positions in the organization.

How do I address this? I want this person to back off but don't want to come off as a doormat, or a complainer. In my last department I would have just told them directly to stop being an ass but here I'm not sure it's the best thing to do. I think that approach will make things worse. I am having trouble clicking and working effectively with them.