I divorced my XH. It's amicable in so far as I am very polite to him, but I wouldn't piss on the cheating bastard if he was on fire, so not really amicable. 
We have a 6yo, and we both now have new b/g friends.
I decided not to tell him because frankly, it's none of his business, and I want contact with him to be as minimal as possible. I knew that my daughter might mention my bf in passing, but I know her well enough to know she wouldn't feel pressured from some secret (it wasn't) and him well enough to know he wouldn't react badly to her if she said something. Although not amicable, we are both happy to be split!
He has a gf now, and hasnt told me. In fact, my daughter hadn't ever referred to her as his gf, so he may not have told her. (he has form for crap like that)
I don't need to meet this woman. Yes, I'm curious about someone spending time with my daughter. But what are we going to do? Chat about the weather for 5 minutes?
What if I dont take to her? Tbh, from the little I know of her, I think we're very different and wouldn't hit it off. But that doesn't make her a bad person. But my ex is hardly going to dump her on my say so, is he?
I have no intention of spending the next x years reporting in to my ex if I get a bf, split up with a bf, etc.
It's not his business, and it doesn't impact my daughter that I don't tell him.