The first thng you need to do is talk to the student. Ask her to stay behind for a few minutes after class or to come early to the next lesson so you have some time together. Don't deal with this conversation in public so the student can keep face.
During the conversation, you will have a number of aims. You need to make it clear which aspects of her behaviour you do not tolerate in your class and ask her to make an effort in this area. Try to get her agreement to make an effort. Be firm but fair and make it clear what will happen if the bad behaviour continues. Keep the conversation focused on behaviour, not the person or the personality.
You also need to find out why the student is behaving as she is. This is not always as easy as it sounds. The reasons can be complicated. It might be that she doesn't understand the work you're doing in class and is ashamed to admit to this. It could also be that she is unhappy in the class due to disagreement with other students. It could also be an issue outside the classroom entirely. Tell the student that you will want to see her again in a few weeks to review the situation.
After this discussion, you need to monitor progress or change. Let the student see you are watching her. Remember to praise any good behaviour and to remind her if she falls back into the old habits. You might decide you want her to sit in a different place to work with other students or to be closer to you. Remember to keep to the review date that you fixed.
It's also a good idea to have a "scale of punishments". This can go from mild punishment, eg extra homework up to an interview with the head. You should keep this scale in your head and use an appropriate punishment for the bad behaviour. In the heat of the moment, if you announce the student has to see the head, it leaves you with nowhere else to go afterwards. It's up to you whether you communicate this scale to the students or not.