In the Generation VII games, the Global Trade Station is accessible via Festival Plaza
The bottom screen while in Festival Plaza shows two large buttons: Battle and Trade. Battle leads to the options Link Battle, Visit the Battle Spot, and Download Rules, while Trade leads to Link Trade, GTS, and Wonder Trade.
To access the GTS in Sun and Moon, you need to go to the Festival Plaza. Once you're there, press the button that says "Trade" on the bottom screen. From there, there should be a button that says "GTS" or something like that. (I'm not actually 100% sure what the button looks like or says myself. I haven't used the Festival Plaza much.)
Sources: This and this.