Similar to the Romulan cloaking device, the Klingons received this technology from the Romulans circa 2268, when the two civilizations shared a political alliance. In 2293 the Klingons tested an experimental Bird-of-Prey that could operate its weapons while cloaked. ...

Why do Klingons use cloaking devices?

The Klingons first acquired cloaking technology in 2268 as part of a technology exchange with the Romulans. In return the Romulans gained access to the designs for Klingon battle cruisers. The cloaking device normally prevents a cloaked ship from firing its weapons.

How did the Klingons get cloaking in discovery?

According to the Star Trek: The Next Generation Technical Journal, the Romulan cloaking device was acquired by the Klingons as an exchange for several D7-class battle cruisers given to the Romulans during the Romulan-Klingon Alliance.