Is it possible to restrict access for certain users to the people directory? If so, how do I do this?
No, it's only possible to hide the People Directory entirely. If you would like to do this, please raise a Support case requesting it.
There is an open feature request for more control over the People Directory at https://jira.atlassian.com/browse/CONF-7837.
I've been researching this issue recently and came across an article on how to do it via editing the Atlassian code in a server instance. It's obviously not for the faint of heart, but will get the job done.
https://confluence.atlassian.com/confkb/how-to-hide-the-people-directory-from-a-confluence-group-720640250.html
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