It is probably worth stating this up front: The relationship you describe has the appearance of an abusive relationship -- and I'm also going to say that I'm sorry you find yourself in this situation :-(
Part of abusive relationships are threats that, in many cases, can or will not actually be realized. While I don't know for sure, my best guess is that your former partner does not actually have much to gain from contacting anyone about your tenure: It would certainly reflect very poorly on them to have been in a relationship with a student, and whatever they would have to say about you would come over as poor taste and sour grapes, not deep insight in your abilities. As such, my best guess is that your former partner is not actually going to pull through with their threat, even if you moved forward with retrieving your possessions with the help of a lawyer.
The second part to keep in mind (and that is something you should definitely take pride in!): Your current department hired you for a good reason, namely that you are qualified in your work! They want you to succeed, and will support you in it. The advice to stay out of contentious topics is probably good, but your colleagues are there to help with get through personal things such as this as they have no stake in it. You will have friends in your current department, or at least people who have good intentions. You can rely on them to find a way through all of this.
My suggestion to be on the safe side would be the following. Write an email to the department head or another senior professor in the department in which you lay out the situation to make sure that it's on record before anyone might hear from your former partner. Maybe something like this:
Dear < department head >
I'd like to bring to your attention a situation that is primarily a personal matter but that might also appear in our professional lives. There is nothing for you to do at this moment, but I want this to be on the written record in case it ever comes up again.
In short, while I was at A University, I was in a relationship with professor X. The end of this relationship was contentious, and I have received threats from X as well as professor Y at B University (with whom he has apparently also had a relationship) that they would try to sabotage my career by writing to you about me.
As mentioned above, there is nothing for anyone to do at this moment. My goal is simply to ensure you know about the threat in case you do get emails from X or Y. When the time comes, in a few years, to thinking about letters of evaluation for the purposes of tenure, I will likely also request that neither X nor Y will be asked to write.
The point simply is to make sure the issue has been recorded in writing before anyone ever gets an email from X or Y, so that if they ever did, they can find the appropriate place for this email: The trash bin. It will also make sure that your department -- which, remember!, wants you to succeed -- will disregard anything coming from the direction of X or Y when it comes time to decide on your tenure. For example, in a faculty meeting about your case, if someone brings up that they heard bad things about you from X, the department head will say something like this: "We will need to disregard what you have just said. A few years ago, user128851 told me some personal details about her time at A university. I can't tell you what they were, but I will share that she and X had disagreements and that X threatened her. I believe that what X is now saying about her is not something we should trust." And just like this, the issue is gone -- the important point is to get out front of anything X might ever say about you.