Con man and cattle thief head off after horse (7)
I believe the answer is:
hustler
'con man' is the definition.
(hustle can mean to trick or defraud)
'cattle thief head off after horse' is the wordplay.
'cattle thief' becomes 'rustler' (synonyms).
'head off' means to remove the first letter.
'after' says to put letters next to each other.
'horse' becomes 'h' (synonyms).
'rustler' with its initial letter taken off is 'ustler'.
'ustler' after 'h' is 'HUSTLER'.
'and' acts as a link.
(Other definitions for hustler that I've seen before include "Illicit dealer (mainly US)" , "Swindler" , "Aggressive dealer" , "Aggressive seller" , "The slur (anag)" .)