The Gun-Free School Zones Act (GFSZA) is a law and requires an act of Congress to repeal it. Knowing how Congress works, that takes more than a day to accomplish. It is quite possible that this could be attached to a National Reciprocity law, which I have personal reservations against (again, knowing how Congress works). A President Trump and the NRA can push Congress quite a bit to accomplish that in 2017.
I wouldn't use The Trace as a source for anything, by the way. The Trace is a notorious anti-gun propaganda machine. I am assuming you are referring to this drivel:
Trump Vowed to Eliminate Gun-Free Zones on His First Day. It’s Not Nearly That Easy. As usual, The Trace is wrong in so many ways. For example, there is
Link Removed, which was published on the same day The Trace published their drivel arguing that Trump "would likely face staunch opposition from other senior military officials" when he tries "to reverse rules governing guns on military bases". Trump isn't in office yet, and the DOD is already changing course.