Famous Young British Artist chap initially ignored (7)
I believe the answer is:
eminent
'famous' is the definition.
(eminent can mean famous or influential)
'young british artist chap initially ignored' is the wordplay.
'young british artist' becomes 'Emin' (Tracey Emin was a Young British Artist).
'chap' becomes 'gent' (I've seen this in other clues).
'initially ignored' means to remove the first letter.
'gent' with its initial letter removed is 'ent'.
'emin'+'ent'='EMINENT'
(Other definitions for eminent that I've seen before include "Noted" , "Exalted in rank" , "Respected; notable" , "Respected; distinguished" , "Famous and respected" .)