How to set up Page Level Permissions in New Google Sites
How to set up Google Sites permissions by Copying Sites
Since settings for page level permissions have not been rolled out for New Google Sites like it was for Classic Google Sites, we must use something very similar leveraging site level permissions. This is particularly important for internal sites or corporate wiki sites where information may need to be private to management or administrators.
Open your Google Site in edit mode via sites.google.com/new
Select "Make a Copy" of your Google Site using the top right three-dot menu
In the copy site menu, under Pages, select Selected page(s)
From here you can select which page, pages, subpages should be under separate permissions
You can decide whether you want to save or delete these pages from the originating site
Now, on this new copy, you can set page level permissions via the Share button in the top right, setting General Access to Private and inviting selected users to view the Google Site
Remember to link the two sites together somehow so users can navigate between the two.
Stay tuned for more information about the release of page-level permissions. Until then we hope this creative uses of the Sharing access for sites will suffice.