Farmer, say, succeeded spreading manure (7)
I believe the answer is:
surname
'farmer say' is the definition.
(Farmer is a surname)
'succeeded spreading manure' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'spreading' indicates an anagram.
'manure' with letters rearranged gives 'urname'.
's'+'urname'='SURNAME'
(Other definitions for surname that I've seen before include "Hereditary identifier" , "Word by which a family is known" , "Family name" , "Family appellation" , "Last appellation" .)