Relative with a name that's sullied (7)
I believe the answer is:
unclean
'sullied' is the definition.
(thesaurus)
'relative with a name' is the wordplay.
'relative' becomes 'uncle' (uncle is a kind of relative**).
'with' says to put letters next to each other.
'a name' becomes 'an' (I've seen this in other clues).
'uncle'+'an'='UNCLEAN'
'that's' is the link.
(Other definitions for unclean that I've seen before include "Dirty, needs a wash" , "Foul" , "Spotted" , "Ceremonially impure" , "Dirty or unwashed" .)