At the end of Chapter 21, Santa forebodingly asks Bernard to contact "him" with the belief that coals in the Dursley's stockings is not enough punishment for giving all of Harry's gifts to the undeserving Dudley.
In the original folklore, Krampus acts not as St. Nick's enemy, but rather as his companion and equal. While Father Christmas would give gifts to good children, Krampus would hunt down naughty children and inflict punishment onto them. The legends differ on what exactly he does to them, ranging from spanking them till blood is drawn with his whip, to kidnapping them to drown them in rivers, even to taking them to Hell where he cooks and eats them for his Christmas dinner.
It is unlikely that the Krampus will be so horrible if he can be contacted and put on commission by Santa, but with the legends as they are, it is likely that Santa only hires him in extreme circumstances.