Jorah has been afflicted with the highly contagious disease known as greyscale for a couple of seasons now, having contracted it when he was trying to bring Tyrion to Daenerys when she was still based in Meereen.
She dispatched him in Season 6 to find a cure for his disease, and we didn’t see him afterward.
From the look of his arm in “Dragonstone,” he was quite clearly unsuccessful in finding that cure.
Still, that one quick scene could be the first hint that a contagion is coming that will result in the deaths of a lot of people.