Nanny runs media organisation (9)
I believe the answer is:
nursemaid
'nanny' is the definition.
(both can mean someone who looks after children)
'runs media organisation' is the wordplay.
'organisation' indicates an anagram.
'runs'+'media'='runsmedia'
'runsmedia' anagrammed gives 'NURSEMAID'.
(Other definitions for nursemaid that I've seen before include "One employed to care for small children" , "child minder" , "Woman tending a child or children" , "her charges are small" , "Girl tending young children" .)