If you use pages which have the state private, they will not be shown in the navigation. Nevertheless it can make sense to show this specific page in the navigation, if you want to provide easy access to this page for your users. The page should only appear to privileged users for sure. I will show you a little hack, which will let you exactly do this.
You have to copy this snippet to your theme at the place where the navigation is.
current_user_can checks, if the current user is privileged to read private pages. If not, then the page will not be shown for him.
Short notice: The 10 at
get_permalink(10) is my ID for the page and has to be changed to your scenario.