Thin cut (6)
'thin cut' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for slit that I've seen before include "Narrow rent" , "Long narrow opening" , "Narrow aperture" , "Long straight cut" , "Long narrow cut" .)
(Other definitions for sliver that I've seen before include "Sharp piece (of glass)" , "just a little bit" , "Wafer-thin slice" , "Splinter of wood" , "Piece cut off" .)