Lady who ran distribution for artist (4,6)
I believe the answer is:
andy warhol
'artist' is the definition.
(I've seen this before)
'lady who ran distribution' is the wordplay.
'distribution' indicates an anagram.
'lady'+'who'+'ran'='ladywhoran'
'ladywhoran' is an anagram of 'ANDY WARHOL'.
'for' is the link.
(Other definitions for andy warhol that I've seen before include "US pop artist" , "Leader of the Pop Art movement, d. 1987" .)