An arm was the upper extremity of a humanoid lifeform.
In 2153, MACO Corporal F. Hawkins' left arm was wounded by a Vulcan crewmember aboard the Seleya. Malcolm Reed later placed a bandage around it. (ENT: "Impulse")
In 2367, Doctor Beverly Crusher initially suspected child abuse after examining Jono and finding evidence of prior serious injuries, two previously fractured ribs, a broken arm, and a low-grade concussion, as well as possible neurological impairment. (TNG: "Suddenly Human")
A sling was a typical first aid treatment for a broken arm. (ENT: "Terra Prime"; TNG: "Who Watches The Watchers", "Relics"; DS9: "The Quickening", "Waltz")
An osteogenic stimulator can be used to treat a broken arm. (VOY: "Resolutions")
Riley Frazier had a prosthetic arm, produced by Orum. (VOY: "Unity")