Within Teamwork, you can set privacy on individual project templates to allow only some users access to these templates.

Note: The project template privacy setting is available on legacy Enterprise subscriptions.

Project template privacy relates to the accessibility of the template itself, and will not make projects created from the template private.

Privacy can be set in the Advanced Options step when creating a new project template

By default, privacy will be set to Everybody who can view project templates.

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Click the current privacy setting to open the privacy modal. Switching between the People and Teams tabs, you can select individual users, entire companies, or teams to apply to the privacy.

Select Update to apply the changes to the template's privacy settings. 

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Note: Only users with permission to manage project templates can create and edit project templates. 

For more information, see: Creating a Project from a Template