The Clips browser is an integral part of the non-linear workflow and thus is always visible in the Cue window.

You can freely drag and drop clips between triggers slots and the Clips browser.

Pick a clip in the library, play it to see if that's what you need, then drag it towards the matrix view and drop to any slot. Please note that dropping a clip onto a slot that already has a clip will replace that clip with the new one.

If you added a clip to a trigger slot by bouncing a region or a range directly to a scene and you like how it sounds, you might want adding that clip to the library. For that, simply pick it from the trigger slot, drag towards the Clips library and drop it there. The file will be copied to the custom library folder and become available for other sessions.