Horsey English pursuit run by Scotsman? (10)
I believe the answer is:
equestrian
'horsey' is the definition.
(equestrianism means horse-riding)
'english pursuit run by scotsman?' is the wordplay.
'english' becomes 'e' (abbreviation).
'pursuit' becomes 'quest' (synonyms).
'run' becomes 'r' (cricket abbreviation).
'by' is a charade indicator (letters next to each other).
'scotsman?' becomes 'ian' (common Scottish name).
'e'+'quest'+'r'+'ian'='EQUESTRIAN'
(Other definitions for equestrian that I've seen before include "Relating to horse riding" , "Jockey" , "Horseman" , "Horse-rider" , "Person on horseback" .)