What to do if your partner starts a relationship with another person without asking for your opinion?? She’s had a lot of relationships that ended badly lately so I don’t want to break her heart again by telling her that she’s not allowed to date that person

Have you two talked about this before? Do you have an existing understanding that you’ll get each other’s opinion before starting a new relationship? If so, then she violated the terms of your relationship, and you need to talk about that. If not, it sounds like you have an expectation that hasn’t been made clear, and you need to talk about that.
I’d sit down with her and say*“hey, it seems like things between you and Cygnus got serious, and we never had a chance to talk about it. That bothers me - can we agree to check in with each other before starting something with a new person?”
If she had asked your opinion, what would you have said? Do you have a problem with this person specifically, or do you just want the security of knowing that in the future, you’ll be able to voice concerns about someone before she gets serious with them? If you have issues with this person, bring those up. If not - if you just want to talk generally about whether*“veto power” is a thing in your relationship - perhaps wait a bit before bringing it up, so she doesn’t feel like you’re trying to establish a position where you put the kibosh on this new relationship.