Approach the relationship with patience. Rebuilding a broken relationship takes time, and you can't expect your partner to trust you immediately afterward. Actions speak louder than words, and it takes time for trust to get built up again.
It depends on how angry you are and if you can be assertive without indulging in anger. That's usually the best approach. If not, don't interact and wait for things...
Check out her body language! Typically, if you feel comfortable, she'll also feel comfortable—it's like a mirror. If you're feeling uncomfortable and awkward, you might be picking up uncomfortable vibes...
Have a frank conversation about it and try having regular check-ins. For example, “Hey, how are we doing with that argument we had where you and my sister didn't see...