It appears the you have restrictions on your device that prevents app downloads and updates. This is done by the organizer of your Family Sharing plan. When the restriction is put in place, then you will no longer see the App Store on your phone. There is nothing you will be able to do to get the App Store back unless the parental control restriction is removed.
If you removed the App Store yourself, then you will find it in the App Library by swiping all the way to the left on your screen. You will find the App Store by searching for it there and can then place it on any of your Home Screens.
Find your apps in App Library on iPhone - Apple Support