Membrane improves a dim graph (9)
I believe the answer is:
diaphragm
'membrane' is the definition.
(diaphragm is a kind of membrane)
'improves a dim graph' is the wordplay.
'improves' is an anagram indicator (I've seen 'improve' mean this).
'a'+'dim'+'graph'='adimgraph'
'adimgraph' anagrammed gives 'DIAPHRAGM'.
(Other definitions for diaphragm that I've seen before include "Partition between thorax and abdomen" , "Midriff" , "Flexible membrane" , "Thin dividing membrane" , "It separates the thorax from the abdomen" .)