Can I get paid for releases of new versions of my app in the App Store?
The App Store doesn't offer support for paid app updates. You can release new features as in-app purchases for the current app (as @Jason said).

If, however, you want to charge for a new version of the app itself, then you need to release the new version as its own app and remove the previous version from sale. A common convention is to name the new app "MyApp 2" (with the "2" as part of the name) to distinguish it, since its actual version number will be 1 since it's a new app. Yes, it's a little confusing...

One issue to be aware of with this approach is that, because MyApp 1 and MyApp 2 are separate apps, users of MyApp 1 won't get any kind of notification that MyApp 2 is available, since it's not an "update" of that app but rather a separate thing entirely.