I have a free and paid version of an app. The free version has limited functionality BUT all the paid functions can be selected. On the paid version, obviously, they work. On the free version, a message is displayed suggesting they try the paid version for those functions to work. Basically, this is what can be done but you can't do it until you buy the full version.
AFAIK, you can not make a free app into a paid app directly. It might be easier to create a separate paid version and enhance that one and use some of the things mentioned above. You can also put adds and splash screens on the free version and advertise that those "annoyances" are not on the paid version.