This guide will let you know how to open the Red Gate in Swordmarch city interior in Xenoblade Chronicles 3. Go through the guide and folllow the simple steps to open it up.
First, you have make your way to the northwest corner of the map.
Once you get there, you will find a ladder and you need to get down to the other side of the red gate by walking around following the platforms. You will get a new quest there and you can unlock the gate which will allow you to go in there.