Xur is back but it's hard to imagine many Destiny 2 players will be thrilled with his inventory this week, especially with the weapon.
Guardians can find Xur in Winding Cove in EDZ this week. Spawn on the location's waypoint, hop on a sparrow, turn left and proceed that way until you reach a fork in the road, pictured below. Then take the right road and go until you reach the crashed Fallen ship.
At that point you can either take the cave or climb up the rocks to reach the vendor.
Skyburner's Oath is the weapon we're getting this week. It's hard to recommend this to anyone so the only reason someone could possibly buy it is to remove it from the sold Exotic Engram pool, provided you don't have all the Exotics from it already.
Hunters can buy Lucky Raspberry which will cause their Arc Bolt grenades to have better chaining capabilities. This is great for clearing large concentrations of mobs in PvE since the Exotic will also recharge your grenade instantly. However, it's not reliable in PvP since more than one Guardian in the same place is not that common and you might not get enough chains to recharge the grenade every time.
Titans are getting Actium War Rig which is fun to use with Auto Rifles and Machineguns. It's not the best choice for any situation but it is certainly the most fun one in many situations. Grab Sweet Business and go nuts in 6v6 Crucible modes or mow down enemies endlessly in PvE. Pairing it with Thunderlord has the potential to cause huge storms.
Warlocks are the only ones getting a particularly useful Exotic for PvP with Karnstein Armlets. These will cause your melee kills, powered or otherwise, to regenerate your health, meaning you will stand a higher chance of surviving a duel that occurs right after one was completed. It is, however, overshadowed by the likes of Ophidian Aspect, Lunafaction Boots and Transversive Steps but that doesn't mean these gloves are bad.