Generally, no.
But there are a few exceptions.
The first exception is if you’re charged with assault on a family member – second offense, which is a felony. Your prior conviction is something the State has to prove and the jury will know about.
The second is if you’re charged with continuous family violence. Because this charge requires two separate instances of family violence within a year, the jury is going to be told about all the alleged assaults that occurred in that year.
The last exception is if you “open the door” to alleged past instances of violence in your testimony. For example, if you testified that you’ve never been violent with the complainant before, the prosecution could put on evidence of other past instances to prove that you’re lying.
Thankfully, in most domestic violence cases, you only need to worry about the current allegation, not anything you may or may not have done in the past.