Strips (6)
(Other definitions for shreds that I've seen before include "Small pieces, maybe of bread" , "Scraps - fragments (of evidence?)" , "Small pieces as of torn paper" , "Rags, tattered pieces" , "Tears into strips" .)
'strips' is the definition.
(paring is a kind of stripping)
This is the entire clue.
(Other definitions for pares that I've seen before include "Shaves pencil to sharpen" , "Sharpens in spare way" , "Sharpens like pencil" , "Trims by cutting away" , "Trims, say a pencil" .)