Noted assertion of right accepted by fab duke (9)
I believe the answer is:
acclaimed
'noted' is the definition.
(both can mean famous or celebrated)
'assertion of right accepted by fab duke' is the wordplay.
'assertion of right' becomes 'claim' (I've seen this before).
'accepted by' indicates putting letters inside.
'fab' becomes 'ace' (both can mean excellent).
'duke' becomes 'd' (abbreviation).
'claim' put inside 'ace' is 'acclaime'.
'acclaime'+'d'='ACCLAIMED'
(Other definitions for acclaimed that I've seen before include "Highly respected" , "Strongly praised" , "Hailed, heralded" .)