Yes, Privacy Policies are always required when using third-party services to collect analytical data about your visitors and website performance.
If your website does not utilize any third-party services for data collection, you are not obligated to have a Privacy Policy. However, it is considered good business practice to maintain a Privacy Policy page for transparency, stating that no personal data is collected, for example.
Be aware that some third-party services, such as Google Analytics, use cookies to gather information about visitor behavior and require a Privacy Policy as part of their Terms of Service. Similarly, Google AdSense mandates a legally compliant Privacy Policy on your website.
You can upload your Privacy Policy in WordPress by selecting "Privacy" under the Settings menu. WordPress also provides a guide with recommendations for content to include in your Privacy Policy, as well as any requirements for your theme and plugins.
Ultimately, it is the responsibility of the website owner to ensure their Privacy Policy contains the necessary information and is both accurate and up to date.