Slur like individual swallowing last of Asti (9)
I believe the answer is:
aspersion
'slur' is the definition.
('aspersion' can be a synonym of 'slur')
'like individual swallowing last of asti' is the wordplay.
'like' becomes 'as'.
'individual' becomes 'person' ('person' can be a synonym of 'individual').
'swallowing' means one lot of letters goes inside another.
'last of' suggests the final letters.
The final letter of 'asti' is 'i'.
'person' placed around 'i' is 'persion'.
'as'+'persion'='ASPERSION'
(Other definitions for aspersion that I've seen before include "No praises (anag) - disparaging remark" , "Malicious remark" , "Defamatory suggestion" , "No praises given to the act of defaming 99)" , "reflection" .)