Shouldn't be a problem, I've always swapped media cards from one device to the next one I get, even when I went from BlackBerry to Android years ago. Fixed that title for you, as well.
Keep in mind, though that if your ZTE phone allowed you to "Move to SD" for an app, those apps won't magically appear on the tablet -- you have to reinstall the app on the tablet itself (and the app data on the card might not be read correctly by the tablet).