Is it possible to re-use pickling liquid?
I would say you could use it once, and probably just to make refrigerator-type, quick pickles.  The problem is that you have no way to determine acidity or salt levels once you remove the previously pickled items. Of course it should look clean and clear.  If you were previously doing a lactic acid fermented pickle, some of the liquid could be used to jump start your next ferment.