You have to first do all the lost sectors on both new destinations normally. Once you do there will be one legend 1250 & One master 1280 that will drop exotics. They rotate daily and the exotics rotate daily. The new exotic armor for all classes is just heads and arms. So if you see the 1250 legend has chess pieces listed it’s only the old exotics. The ones that offer the head and arms will still give you old exotics but that’s where you will find the chance to get the new ones.

The new exotics only drop from special beyond light lost sectors, activated from a beacon next to the sector entrance. The chest at the end after fighting through champions and the boss will have a chance at the new gear.