I'm sorry this is happening, this just happened to us.
Your daughter's new "friend" is what's known as a "third party." She is intentionally leaving your daughter out, perhaps she is afraid that the other girls are going to be better friends with your daughter and leave the new girl out.
Your daughter needs to HANDLE the situation, not just walk away. However, she will need to come to you in order for you to help her, so if she's looking for advice, now's the time to help. If she's not, then there isn't much you can do.
My daughter just went through this, and now the situation is handled. She is also 11, I guess this is the age it happens!
First talk to your daughter about some specific situations. Then you can help her find ways to handle them and you can even act them out with each other so she can practice. For example, what does your daughter do when the other friend yells at her? There are ways she can handle the yelling friend. Your daughter can say "Why are you yelling at me in front of my friends? That isn't very nice."
If the girls hang out and "privately talk" without your daughter then your daughter and walk up to the group and say "I'd love to hang out and talk with you all. Can I join in?" If the mean girl says "No!" Then your daughter can say "Why are you purposely leaving me out? I thought we were all friends."
The point is for your daughter to confront the Mean Girl and point out what she is doing. Mean Girls don't like that.
This is what my daughter did, and now she is no longer left out. The mean girl actually cowered (most of them do) and she knocked it off. The Mean Girl in my daughter's group actually stopped picking on my daughter and chose a different person in the group of friends to be mean to. My daughter has been standing up for this girl too. I don't know why they all still hang out with Mean Girl, but girls will be girls.
My daughter also took each friend aside by themselves and said "You and I have been friends for a while, and it hurts my feelings when you leave me out on purpose or let Mean Girl yell at me. Have I done something to upset you?"
It turns out the other friends didn't quite realize what was happening. They knew, but they were so young that they just didn't see the mechanics of it.
Your daughter can be assertive, or she can walk away.
I wish you luck, this will probably continue to happen all through her life (and even into adulthood!)