Within Teamwork.com, you can set the privacy on a task list so that only certain people on the project are able to see it.
When a task list is made private, all tasks in the list will inherit the privacy you have set for the task list.
Setting privacy on a new task list
When adding a new task list, you can choose who to make the list visible to via the Privacy tab. By default, privacy will be set to Everybody on the project.
In the privacy modal, you can switch between people and teams. Privacy can be set to individual project members, entire companies, or teams.
You can use the search field at the top to locate specific people. Click the filters button on the right for additional options on who should be selectable in the People and Teams tabs.
Editing task list privacy
You can edit the task list privacy via the task list options menu. In List or Table view, click the three dots to the right of the task list name and select Edit List from the dropdown menu.
In the task list settings, go to the Privacy tab where you can select which people to include in the privacy.
Site administrators in the owner company can see private items, regardless of any privacy settings.
If you are editing an existing task list that is open to everyone on the project, but some of the tasks on it are individually marked private, you cannot mark the task list as private unless you remove the privacy settings on those tasks first.
For more information, see: Task List Options