The GDPR requires you to inform people about the processing of personal data. This therefore includes your employees, interns, work-study students, corporate officers as well as managers.
How should these individuals be informed? You must inform them via a privacy policy that covers all data processing carried out by your organization.
Does the privacy policy need to be signed? You don't need to have the policy signed. You just need to inform people and have proof that you have done so.