This question might be off topic, but I wanted to ask the fellow developers.
Is there a way on Google play I could change my free app to a paid app?
What would happen to the existing users if it is allowed? Would they be asked to pay when the new update is available?
You could add in-app payment processing to your free app and charge for enhanced features. Per
http://support.google.com/googleplay/android-developer/bin/answer.py?hl=en&answer=1153479
"By using the in-app billing feature you can add revenue-generating features to your applications, enhancing the revenue potential of paid applications and turning free applications into new revenue sources."
Now, could you disable functionality that was already available in the free app, and then charge via in-app payments to have it restored? Technically I do think it could be done, since you are in control of your implementation of those features, although you would have to investigate whether that would be a violation of Google's policies.
However, doing it might alienate your users, and if word got around they might even stop updating your app to avoid the "trap." So a much better approach would probably be to add enticing new functionality that enhances the existing functionality, and then charge for it.