S.K.
As far as I can see, there is no reason for them to know you signed a lease right now. When you are moving, you can tell them. After all, the house is being prepared to be sold, they have to know you have to move at some point & when that is impending, that is the time to tell them.
I understand the points made about maintaining trust. Trust requires that they know where you are & what is going on. Not your exact plans for the future. Right now, you are at the house & you are getting it ready for sale. They know that - trust is kept. When it is time to move, you tell them that.
At some point, your ex will have to know where you are so paperwork can be exchanged, etc. Doesn't mean he should be riding by.
I agree, don't borrow trouble right now if you don't need to. Wait until they have to know.