This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The range extender was a portable Emerald Chain tool used by couriers for amplifying weak signals within subspace. These tools saw their greatest use in "pockets of the galaxy where subspace relays were few and far between". Cleveland Booker, ex-courier for the Emerald Chain, described having a range extender as one of the benefits of having the job.
Two years later, while on aboard the USS Discovery, Paul Stamets' engineering team had difficulty with getting a signal via long-range sensors to the crashed KSF Khi'eth in the Verubin Nebula. Their signal did not have the strength, even when juiced with additional power, for getting through the static at the space-subspace barrier. To make himself useful to the ship, Booker loaned the team his range extender, which solved the problem. Upon confirmation of the signal holding, the Discovery began receiving data from the Khi'eth. Later that day, Captain Saru, in his conversation with Fleet Admiral Charles Vance, recognized Booker's contribution in getting the Discovery access to the systems of the Khi'eth. (DIS: "Terra Firma, Part 2")