A little African-American celebrity (4)
I believe the answer is:
name
'celebrity' is the definition.
(as in a 'big name')
'a little african-american' is the wordplay.
'a little' indicates a hidden word (a little bit of the clue).
'NAME' is hidden in the letters of 'african american'.
(Other definitions for name that I've seen before include "Title; famous person" , "Designation - reputation" , "Appoint - famous person" , "Monicker" , "By which one is known" .)