It isn't Miliband that's famous (5)
I believe the answer is:
noted
'famous' is the definition.
(noted can mean well-known or famous)
'it isn't miliband' is the wordplay.
'it isn't' becomes 'not' (I can't justify this - if you can you should give a lot more credence to this answer).
'miliband' becomes 'ed' (politician Ed Miliband).
'not'+'ed'='NOTED'
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for noted that I've seen before include "Illustrious" , "Having renown" , "Observed - recorded" , "remarked upon" , "Toned (anag.)" .)