Can I record a private note about a candidate as well as their current salary, but not let the rest of the team see it?

Yes. The Private tab on a candidate's profile is the best location for sensitive candidate information, such as salary details. The Private tab includes a section for custom candidate fields marked as private, as well as a section for private notes

Site Admins with the user-specific permission Can see private notes, salary info, manage offers, request approvals, and approve jobs/offers can access the entire Private tab. 

Job Admins with the permission stripe Can view and edit private candidate and application fields can access custom candidate fields marked as a private, and Job Admins with the permission stripe Can view and create private notes can access private notes.

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