Tyranids eat man , elder , orks and Tau ( and anything else that's eatable )
Chaos dies ( nothing to sustain them )
Necrons sit and wait till the tyranids either starve ( or turn on themselves to sustain higher hive creatures ) or bugger off .
Necrons are now the rulers till the destroyers get bored and decide to anhialate the last living remanants ( ie , the other Necrons ) .
simplistic I know , If you follow the fluff though the silent king came back from his self imposed exile once he realised the threat of the Tyranids .
If they ate all life then the Necrons would not be able to return to biological beings ( so he started to awaken tomb worlds ) . So in all liklyness theyd probably fight and ally against the Tyranids . That's not to say some dynasties would abstain as all don't want to return to what they once were .
I also like the idea that at some point the C,Tan regain there former self,s , either through
Necron memory engrams breaking down ( and not remembering whats captured in the teserct labrynths or why they did it ) OR they do manage apotheosis ( I think that's what they call becoming mortal again ) and as with mortals , time turns fact to myth and curiosity eventually kills the cat