Someone's arm that is unable to fully extend or function
Guy 1: "Hey, why is Chris shooting with his left hand? I thought he was right handed."
Guy 2: "Yeah, he has a gimp arm, it can't fully extend."
When cuddling, the useless arm that gets stuck in between the two cuddlers due to the lack of a better place to put it. Usually ends up by the crotch, intentionally or not.
"Are you trying to grope me?!"
"No, it's just gimp arm."