The Sturm is one of the unique weapons you can gain by performing specific tasks in the game. In addition to improved revolver parameters, such as a magnified magazine size, reduced weapon recoil, or increased range, it has an additional feature: the connection to the Drang sidearm - when you use it, you increase the power of Sturm's precision shots and replenish the ammo used by Sturm. Make sure to use both of these weapons interchangeably (especially on the Hunter class).
To start the path to the revolver, but also to Drang, you must go to Nessus and perform all missions marked with a dark blue icon and a white crown in the middle. You will be given a legendary pistol after completing all missions in the series, but if you lose/dispose of it, you can re-purchase it from Tyra Karn at the Farm.
Completing tasks on Nessus also supplies an object for Master Rahool in the Tower. He will send you off to face a series of challenges. The first two are not difficult, but they can be a bit time consuming: you have to kill 10 Fallen using the previously acquired Drang sidearm, and decode 1 exotic engram and 5 legendary engrams for Rahool. These must be the engrams, which you have in your inventory, the ones gained for reputation are not relevant here. A good way to acquire new engrams is to face each of the more difficult opponents, who appear randomly in certain locations (mini-bosses with dark orange health bars), from time to time.
The third challenge is activated when you return to Rahool after finishing the second one and after relaying the message to Tyra Karn at the Farm. You now have to go to Nessus, where you have to make 10 double kills - in which you dispose of two Fallen opponents without reloading. In addition, you have to get rid of 10 powerful Fallen, who supervise the smaller units and have a yellow health bar. You will find them amongst larger groups of enemies on the map or during Public Events with the Fallen. Important: Both of these goals must also be accomplished using the Drang pistol.
The fourth step towards acquiring the Sturm (after returning to Tyra from the previous challenge) is the completion of the Exodus Crash Adventure. You can do this task yourself and it does not need to be 100% complete to qualify as a stepping stone along the path to the weapon. After completing it, meet with Tyra Karn on the Farm again, and you will receive the Sturm hand cannon.