Vileness, putrid, spreading in a day (9)
I believe the answer is:
turpitude
'vileness' is the definition.
(thesaurus)
'putrid spreading in a day' is the wordplay.
'spreading' is an anagram indicator.
'in' is an insertion indicator.
'a day' becomes 'tue' (abbreviation for Tuesday).
'putrid' anagrammed gives 'rpitud'.
'rpitud' inserted inside 'tue' is 'TURPITUDE'.
(Other definitions for turpitude that I've seen before include "Baseness, depravity" , "corruption" , "Depravity, wickedness" , "Depraved or wicked behaviour" .)