Equine event in Dorset’s regularly visited — wise (8)
I believe the answer is:
dressage
'equine event' is the definition.
'dorset's regularly visited wise' is the wordplay.
'regularly visited' indicates alternate letters (letters are taken at regular intervals).
'wise' becomes 'sage' (similar in meaning).
The alternate letters of 'dorsets' are 'dres'.
'dres'+'sage'='DRESSAGE'
'in' acts as a link.
(Other definitions for dressage that I've seen before include "Art of horse training" , "Method of horse training" , "Event for rider" , "Riding skill" , "equestrian activity" .)