Hi areej209,
Welcome to Apple Support Communities. I understand you're unable to access Private Browsing in Safari. I'll be happy to help. First, I'd recommend checking to see if there are any Content & Privacy Restrictions enabled on your device in Settings > Screen Time: Use parental controls on your child's iPhone, iPad, and iPod touch. If Content & Privacy Restrictions are enabled, it's expected that tapping "Private" in the Safari app will have no response.
If you don't have Content & Privacy Restrictions enabled in Screen Time, and Private Browsing in Safari is still not responding, I suggest to force close Safari. From there, please open Safari and see if you're able to access Private Browsing without any issue. If needed, here's a helpful article on how to properly force close an app: How to force an app to close on your iPhone, iPad, or iPod touch If that doesn't help, the next step is to restart your iPhone and see if that helps: Restart your iPhone, iPad, or iPod touch
Best Regards.