How soon after a bad relationship can you start dating again? Single moms? Single Dads? Single period...

My ex is threatening to kill me because I moved on and he’s making me feel like it’s too soon to date. I’m not bringing him around my kids or anything we just go out and chill and my babysitter watches them when I go on dates. He’s Mad because I don’t want him. He didn’t do nothing for me. Wasn’t respecting my boundaries. Cheated on me and now I’m having fun and he’s harassing me make threats to kill me? What should I do? I already called the police