There are two possible solutions that immediately spring to mind.
1. When you apply a graphic style to a clip group (or a layer), the styles may appear BENEATH its contents - and the effect is therefore entirely hidden.
You can re-order the contents/effects so that your graphic style is applied on top - do this via the appearence panel. Here's an example;
Here you can see that there is a graphic style applied (green and yellow pattern) - but that it's not visible, and instead we're seeing the blue patterned contents.
In the appearance panel, 'Contents' appears ABOVE the two fills that have been applied (as a graphics style) to the layer.
Compare that to the following picture ..;
By dragging the contents below the fills (and/or strokes, etc, if applicable), the graphic style is now visible.
2. Your other option is to apply the graphic style to your contents - as opposed to the layer or clipping mask. The simple way of doing this if the layer or clipping mask is selected, is to click on the 'Edit Contents' button (see the image below).
You will most likely find that graphic styles will now work as expected (famous last words ...).
If you look in the appearance panel, you will see that your selection will have changed to one or more of your content items - and the graphic styles will be applied directly. It may be that you DON'T want to apply the styles to your contents, but if this is not an issue (or is otherwise desirable), this is an easy way to accomplish this.
Hope this helps.