Less well-bred horse picked up (7)
I believe the answer is:
coarser
'less well-bred' is the definition.
(coarse can mean vulgar or ill-bred)
'horse picked up' is the wordplay.
'horse' becomes 'courser' (a very fast horse).
'picked up' indicates a 'sounds like' (homophone) clue.
'courser' is a homophone of 'COARSER'.
(Other definitions for coarser that I've seen before include "Comparatively crude" , "less refined" , "A scorer (anag.)" , "More vulgar" .)