You can not, and should not replace your free app with the paid version.
Unless you do a in-app to unlock the free app, the best practice seems to be to create a "key" app which unlocks the functionality in the free app. This key app can be hidden from the app drawer, which should prevent the annoyance usually associated with having two apps.
Another benefit of this is that all user data remains within the free app, and once the user upgrades to pro, you do not have to take any further steps to move the data from free to pro. Also, even if the user uninstalls the pro key app, the data will still remain in the free app.
Take a look at this answer for the simplest way to do the check for a key app from your free app - there are many ways to do it, this is just a basic example.