They happen to involve equestrianism (6)
I believe the answer is:
events
'they happen' is the definition.
(I've seen this before)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for events that I've seen before include "Important happenings or incidents" , "matters" , "Incidents, occurrences" , "Occurences, happenings" , "Things that happen" .)