"Brother Hadley" was the older brother of Remy "Thirteen" Hadley and Amy Hadley, and the oldest child of John Hadley and Anne Hadley. Like his mother, he developed Huntington's disease. He was an unseen character.
All that his known of Thirteen's brother is that he was somewhat older than her and, by the beginning of Season 7, he was suffering from the late stages of Huntington's. Thirteen mysteriously took leave in Now What? and led the rest of the team to believe she was trying an experimental treatment. It appears she instead left to take care of her brother.
Her brother had little control of his emotions or movement, and when he was lucid begged Thirteen to kill him. Although she wore gloves to prevent anyone from proving she gave him a lethal dose of narcotics, she couldn't hide the fact that she requisitioned the drugs. As a result, she was sent to prison for improper prescribing.
She hides the reason she was in jail from Gregory House when he comes by to pick her up when she was released, but from her use of "us" when talking about her family, he deduces she has siblings he didn't know about. Thirteen then breaks down and admits she killed her brother.