According to the latest from Game Informer, which has the month-long scoop on the expansion, acquiring the Khvostov 7G-OX will work similar to how you earned the Sleeper Simulant.
Players will come across parts for the weapon in the Plaguelands, and will be located in chests or handed out as a "random reward" for taking part in the Archon's Forge battle arena.
Find one weapon part, take it to the quest giver, and the Exotic quest chain will kick off. Players can also save some search time by dismantling the Khvostov they already have - if it hasn't been scrapped already.
There's more through the link and in the video from Arekkz above.
Destiny: Rise of Iron released on PS4 and Xbox One September 20.