Delete Developer beta profiles
First, you have to delete the iOS 16 Beta Software Profile that you’ve downloaded from the Apple Developer Center or from BetaProfiles.com.
Go to Settings - General - VPN & Device Management and tap the Beta Software Profile that appears. Tap Remove Profile. If asked, enter your device passcode, then tap Remove. Then restart your devices for the changes to take effect.Check out the Unenroll page for details →
Download Public beta profiles
Your device will notify you when the profile has been downloaded. Open Settings, tap the profile and follow the onscreen instructions to allow installation.
That's it! And the next time there is an update to the public beta you should get the new build under the public beta portal.