A splint was an ancient medical concept that uses two flat pieces of wood or plastic, wrapped with a bandage to keep a broken bone immobile. According to Doctor Katherine Pulaski, it was a time-honored way of practicing medicine "with your head, your heart, and your hands." (TNG: "Contagion")
Upon returning to Enterprise in a shuttlepod after having a rock climbing accident on Risa in 2152, Ensign Travis Mayweather had his right leg in a splint. (ENT: "Two Days and Two Nights")
This splint isn't referred to as such in the episode; the name comes from the final draft script of "Two Days and Two Nights". There, it was described as "a high-tech alien splint."
The crew of the USS Enterprise fashioned a splint to hold the bone while they carried the miniaturized Hikaru Sulu to sickbay after he fell from his controls and broke his leg. (TAS: "The Terratin Incident")
By the 23rd and 24th centuries, the favored form of technology used to repair broken bones became the bone-knitting laser, or knitter. (TAS: "The Terratin Incident"; TNG: "Contagion")
Quark made a splint for Odo's leg after it was broken on a Class L planet they were stranded on in 2373. (DS9: "The Ascent")