Renting an apartment. Moved into another unit in another part of the city to get away from an ex that was giving us problems. The apartment manager knew why we moved and the new apartment was run by the same manager. She told to ex where we moved. Then when she let us out of the lease she told him that too. What can I do?

What do YOU want to do ?
You have no expectation of privacy in this situation, unless you specifically asked for your new address not to be divulged. Even then there is no legal recourse available to you.

What "privacy act"? Laws vary by area and since you neglected to provide your general locale, we can't even tell you if there is a privacy act that applies. There is a feeling, at least in the US, that there are laws guaranteeing privacy, but that's not the case. There are laws that control what certain types of businesses do with your information, but there is no general privacy act.

As Ben notes, unless there was a signed agreement not to provide info, I don't believe any law was violated. On the other hand, if the ex is harassing you (or gets violent, god forbid), you might have a case against the manager for aiding and abetting.

You learn that people will and can find you, if you move, I is going to happen.