You can set access to your Google Site to control who can work on the unpublished version of the site and who can view the published version. Each person that you give access to the site can be set as an editor or a published viewer.
To set site access, click on the Share button near the top-right corner of the screen.
To share the site with specific people only, click in the Add people and groups box and enter the name or email address of each person you want to share the site with, separating each email address with a comma
Choose whether all people added will be able to edit or to view published site
An email notification of the share will be sent, providing the invitees with a link to access the site - you can type an optional message in the Message box
Click on Send
Click on the Cog in the top-right corner of the Share screen to choose whether site editors can publish, change permissions and add new people to the site.
You can also choose how people can view the current draft or published copy of your site:
Click on the Share button
Click on the Change link along the bottom of the dialog box
Choose who can view the draft and published site - this can be anyone, anyone in the organisation or only the people specifically named in the Share dialog box
Click on Done
If you have shared the site with everyone in the organisation, click on the Settings button in the Links dialog box to chosoe whether people in the organisation can search for the site in Google Drive.