You can have all new posts created by instructors and students default to private by navigating to the Manage Class tab and clicking on the Customize Q&A tab. Make sure private posts are set to Enabled and select Private Posts as Default:
You can have students only post privately to you, which can be helpful if you would like to approve student posts before making them visible to the entire class. Students will not have the option to post to the entire class. If you want to share a private post with the rest of the class, you can change that post into an anonymous public post for the whole class. To learn about changing the visibility of a post, click here!
When you're done, be sure to click the Save Changes button.