Champion Irishman is without doubt not unknown (9)
I believe the answer is:
conqueror
'champion' is the definition.
(thesaurus)
'irishman is without doubt not unknown' is the wordplay.
'irishman' becomes 'Conor' (common Irish name).
'is without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'doubt' becomes 'query' (a query is a doubt or question).
'not' indicates named letters should be taken away.
'unknown' becomes 'y' (algebra).
'conor' enclosing 'query' is 'conqueryor'.
'conqueryor' with 'y' taken away is 'CONQUEROR'.
(Other definitions for conqueror that I've seen before include "William's title after 1066 battle" , "William of Normandy" , "Victor, winner" , "Military victor" , "humbler?" .)