On your ipad apps page just keep your finger pressed on your old radio app until all the apps wobble,Then press the x on the radio app and this will remove it as it may have been corrupted or is Incompatible after the software update then press the home button to stop the apps wobbling.

http://www.dummies.com/how-to/content/how-to-work-the-ipad-buttons.html

Re software update you should be using IOs8 (2)http://support.apple.com/kb/DL1758

Then go to the Apple App Store App on you ipad.

At the App store download the FREE app.  https://itunes.apple.com/gb/app/air-radio-lite/id650795675?mt=8

It's a simple radio app that works great. You just press the desired station and it plays in an instant no tuning required. All the UK stations BBC Radio 4, 4extra, Classic FM, Talk sport etc
If you do not like that or would like more apps just place "Ipad Radio" in the search box top right on the App store page and you have a large choice both free and paid apps. Remember you can have as many radio apps as you like on your ipad.  :) :) you may have to use your VPN.