Meant improvement about role that's flat (9)
I believe the answer is:
apartment
'flat' is the definition.
(I know that flat can be written as apartment)
'meant improvement about role' is the wordplay.
'meant improvement' becomes 'ament' (I can't justify this - if you can you should believe this answer much more).
'about' indicates putting letters inside.
'role' becomes 'part' (eg a part or role in a film).
'ament' placed around 'part' is 'APARTMENT'.
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for apartment that I've seen before include "Flat (mainly US)" , "quarters" , "Suite of rooms to live in" , "place to live" , "Set of rooms or American flat" .)