An anodyne relay is a device used for various purposes on Federation starships.
In 2372, the USS Voyager came across Pralor Automated Unit 3947 damaged in space. Lieutenant B'Elanna Torres connected a series of modified anodyne relays to its chromodynamic power module, which allowed her to infuse warp plasma into its energy matrix. (VOY: "Prototype")
When Neelix had a problem with a thermal array in his galley later that year, Samantha Wildman noted that he needed a new anodyne relay. (VOY: "Deadlock")
In late 2374, there was a minor malfunction aboard Voyager. Tom Paris bet that the anodyne relay was responsible, while B'Elanna Torres said it was a plasma conduit. Paris won, and had Torres join him in the Klingon martial arts program. (VOY: "Distant Origin")