Firstly - be very careful using 'shit'. It is a very offensive word. To me, it sounds like very ignorant language, so it's a little hard to say. I think that the 's***' is referring to 'things', so it means something like 'keep everything quiet from now'.

This is very colloquial. "Like" is being used as an interjection, or filler word. It doesn't have any meaning here. "Shit" is frequently used in American English as a vulgar way of saying "things," "stuff," or "situation." So this sentence means "How about keeping everything quiet from now on?"