Run a piece about hedonist (9)
I believe the answer is:
epicurean
'hedonist' is the definition.
(I've seen this before)
'run a piece about' is the wordplay.
'about' indicates an anagram.
'run'+'a'+'piece'='runapiece'
'runapiece' is an anagram of 'EPICUREAN'.
(Other definitions for epicurean that I've seen before include "enjoyer of fine food" , "pleasure-seeker" , "foodie" , "one sensuous and Greek" , "Given to sensual enjoyment" .)