Going on horseback in part of Yorkshire (6)
I believe the answer is:
riding
This clue is a triple definition!
'going' is the first definition.
(riding is a kind of going)
'on horseback' is the second definition.
(I've seen this before)
'in' acts as a link.
'part of yorkshire' is the third definition.
(term for a regional division of Yorkshire)
(Other definitions for riding that I've seen before include "Canadian constituency" , "Establishment teaching horsemanship" , "On top" , "being carried" , "Establishment teaching equestrian skills" .)