Thin sheet surrounding body parts (8)
I believe the answer is:
membrane
'thin sheet surrounding body parts' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for membrane that I've seen before include "Tissue layer" , "Thin sheet that surrounds body parts" , "Layer surrounding cells" , "Thin sheet surrounding body parts" , "Thin pliable sheet of material" .)