If the child is talkative, but unwilling to share in front of others, I find that putting them in small groups with outgoing students can really help with their communication. Sometimes it takes becoming friends and being comfortable with the people around for shy or quiet children to be able to participate in large group discussions. Having even just one outgoing friend can greatly boost the confidence of the shy child. Watch who the child communicates with, or what they are comfortable doing during different activities. Use this information to help make the child feel more involved and safe in the classroom during large group discussions.
If the shy child is not talkative, give them space. Let them become comfortable in their environment and take things slow. It can take shy or quiet children longer to become comfortable enough to share in front of the class, and I would not do anything that would cause them to feel embarrassed (for example calling on them if they don't have their hand raised). When you see outgoing behavior, reward it and encourage them to express their thoughts more often. Saying something as simple as "that is a great thought 'Tommy'" or "I really like how you raised a quiet hand 'Susan' what would you like to add?" will show the child you noticed they had something of value to contribute to the group and encourage them to continue participating.
Shy children, in my experience, usually take much longer to open up in the classroom setting, but once they feel safe, comfortable, and have a sense of belonging, their behavior changes in leaps and bounds. It will take time. Allow the child to participate and open up on their terms. Reward outgoing behavior, and you will soon see them becoming more talkative and wanting to be apart of the conversations and large group activities.