If you collect personal information, then yes, you need a privacy policy.
Unlike a terms and conditions statement, a privacy policy is legally required in many countries, including Australia, the USA, and all EU nations.
You'll also find that many third-party APIs and services require you have a privacy policy. Some services that require a privacy policy are Meta ads and Instagram ads, Google Ad Sense, and the two major commercial app marketplaces: Google Play or the App Store.