App not opening in full screen on iPad

Some Apps designed explicitly for iPhone will not fill the larger screen of the iPad - unless the App is explicitly coded to utilise the full screen of the iPad. Where applicable, this App-limitation, cannot be bypassed.

You might contact the App Developer and enquire as to the possibility of the App being updated to use the iPad's full screen:

How to contact an app developer - Apple Support

As previously, some apps are iPhone only but will run on the iPad. There is usually at the bottom/right of the app an icon to blowup the app to full screen.

When buying apps it will tell you what devices the app is made for…

What app is it? Not all apps are optimized to use the full screen of an iPad.