Layers separated by right tool (6)
I believe the answer is:
pliers
'tool' is the definition.
(pliers is a kind of tool)
'layers separated by right' is the wordplay.
'layers' becomes 'plies' (ply is a kind of layer).
'separated by' indicates putting letters inside.
'right' becomes 'r' (abbreviation).
'plies' placed around 'r' is 'PLIERS'.
(Other definitions for pliers that I've seen before include "Hand tool used for gripping" , "Wire benders" , "Gripping tool, kind of pincers" , "Kind of pincers with flat gripping surfaces" , "Gripping tool with two serrated jaws" .)