Famous but unwell American group comes to us (11)
I believe the answer is:
illustrious
'famous' is the definition.
(I know that celebrated can be written as illustrious)
'unwell american group comes to us' is the wordplay.
'unwell' becomes 'i'll' (similar in meaning).
'american' becomes 'us' (abbreviation for United States).
'group' becomes 'trio' (a group of three).
'comes to' means one lot of letters go next to another.
'ill'+'us'+'trio'+'us'='ILLUSTRIOUS'
'but' is the link.
(Other definitions for illustrious that I've seen before include "Eminent" , "Distinguished, renowned" , "Highly respected, well known" , "Celebrated" .)