Welcome to iMore! Try swiping the app store out of multitasking. Click the home button twice, then find the app store and swipe it out. Then do a hard reset.
Hold the power/wake button and the volume down button at the same time until the Apple logo appears. Then release.
Hold the top or side power/sleep button and the home button at the same time until the Apple logo appears, then release.
You can also try to sign-out & sign back into iTunes/icloud in settings. Is your data or wifi working correctly? Is your phone uptodate with the latest updates? Just some thoughts, let us know what happens when you try these things. Cheers