I simpered about a bit of skin (9)
I believe the answer is:
epidermis
'a bit of skin' is the definition.
('epidermis' is part of 'skin')
'i simpered about' is the wordplay.
'about' indicates anagramming the letters.
'i'+'simpered'='isimpered'
'isimpered' anagrammed gives 'EPIDERMIS'.
(Other definitions for epidermis that I've seen before include "Surface of the skin" , "Outer layer of skin" , "Protective covering" , "Outermost layer" .)