Add a really simple version of a Under Construction page to your website by enable this plugin. Use IP to restrict all users except the whitelisted addresses.

Go to the settings page in Settings > Really Simple Under Construction. Enable by checking the checkbox. The Under Construction site is only visible if not logged in. Optionally you can set three things:
1. Customize the Under Construction site by adding plain HTML that will be displayed.
2. Set the secret key to be able to by-pass the Under Construction page.
3. Set for how long the by-pass should work.
4. Add IP addresses for whitelisting a users or services.