You cannot make a Facebook Page fully private
Facebook Pages are public by design
You can limit who sees some content by adjusting Page settings
Go to your Page
Open Settings
Check Audience and Visibility options
Restrict country or age access if available
Hide the Page from search engines if the option is available
Remove the Page from public visibility by unpublished status if you want it not to be visible
Use a private Facebook Group instead if you need a private space
Set the Group to Private in Group settings
Control who can join the Group
Limit who can see posts in the Group