One of the most frustrating things is to have a rug on top of carpet not lying flat. Many rugs on carpet wrinkle, buckle and creep. This does not look good and causes premature wear to the rug. It is important to keep all rugs as flat as possible on carpet.
There are thin, sticky rug pads that claim to be for rugs on carpet. These sticky pads are inexpensive and do not work. A rug pad for a rug on top of carpet should be stiff and dense to resist foot traffic and furniture weight. The thin sticky rug pads are not dense at all and will move with weight.
One of the best rug pads for rugs on carpet is called No-Muv rug to carpet pad. No-Muv is made only for use under area rugs on carpet and truly does work. No-Muv is 1/4 of an inch thick and has a stiffened lower side to grab to your carpet and prevent creeping. The upper side is a dense felt which holds the area rug and prevents wrinkling and buckling.