Equestrian pursuit in part of Yorkshire once (6)
I believe the answer is:
riding
This clue is a double definition.
'equestrian pursuit' is the first definition.
(equestrian pastime or pursuit)
'part of yorkshire once' is the second definition.
(eg the West Riding of Yorkshire)
'in' is the link.
(Other definitions for riding that I've seen before include "Establishment teaching equestrian skills" , "Horsemanship - once a third part of Yorkshire" , "Division of Yorkshire" , "Establishment teaching horsemanship" , "Third Division" .)