Swipe down on the Home Screen and use Spotlight Search
Check the App Library by swiping left past the last Home Screen page
Open the App Store and search for the app name
Check if the app is hidden from the Home Screen by long-pressing the Home Screen and tapping Edit Home Screen
Go to Settings > Home Screen and App Library to review app display options
Check Screen Time > Content & Privacy Restrictions > Allowed Apps
Check Screen Time > Content & Privacy Restrictions > iTunes & App Store Purchases
Check if the app is inside a folder on the Home Screen
Check the Purchased list in the App Store
Restart the iPhone and search again
Update iOS if the app still does not appear