Re: Need fo Speed: No Limits lost data

The update that No Limits had was only supposed to reset your game progress.

Link: Need for Speed No Limits - Support Announcements

There is a way to recover your game data in No Limits if you were previously logged in Google Plus before it happened. However, since you weren't logged in to Google Plus before it happened and that you removed No Limits and installed it again, your game data is lost forever!

Link: Save Data & Cloud Issues: Lost Data and Game Progress

Either you start over in No Limits or you uninstall No Limits for good and forget about it. It's your choice.