Why does my app store keep saying tap continue but I haven’t seen any continue button

Welcome to the Apple Support Communities!

I understand you are having an issue with the App store on your iPhone. Are you trying to purchase an app or download an app update? What were you doing when you saw the request to Continue? I'm assuming you swiped up to see the bottom of the page on your iPhone display?
If all else fails, I would suggest pressing the Home button twice to show all of your open apps (including the App Store) and then swipe up to close it.
How to force an app to close on your iPhone, iPad, or iPod touch
Next, check to make sure the payment information for your Apple ID is up to date, even if you are downloading a free app or an update.
Change or remove your Apple ID payment information
You may need to input your card's expiration date and CVV number while you are in this window. Check to make sure your billing address matches what is on your bank statement. Then tap Done.
Now, restart your iPhone, open the App Store app, and try the purchase or download again.
Auriana, if this does not resolve your issue, please reply with any additional information you can about what you are trying to accomplish, and I'll do my best to help you!
Take care.