Relative has a name for being grubby (7)
I believe the answer is:
unclean
'being grubby' is the definition.
('unclean' can be similar in meaning to 'grubby')
'relative has a name' is the wordplay.
'relative' becomes 'uncle' (uncle is a kind of relative).
'has' means one lot of letters go next to another.
'name' becomes 'n' (common abbreviation e.g. on forms).
'uncle'+'a'+'n'='UNCLEAN'
'for' is the link.
(Other definitions for unclean that I've seen before include "(Ritually) tainted" , "Infected" , "taboo" , "Foul" , "Defiled" .)