Set off briefly, grabbing a sheet (4)
I believe the answer is:
leaf
'sheet' is the definition.
(I know that leaf is a type of sheet)
'set off briefly grabbing a' is the wordplay.
'set off' becomes 'left' (set off can mean to leave).
'briefly' means to remove the last letter.
'grabbing' indicates putting letters inside.
'left' with its final letter taken off is 'lef'.
'lef' enclosing 'a' is 'LEAF'.
(Other definitions for leaf that I've seen before include "See 1" , "Thin sheet of metal" , "needed for making a longer table" , "Page or piece of foliage" , "Bit of tree, of book" .)