Hi,
https://www.openstreetmap.org/way/1385736096 does not look like a riding centre (leisure=horse_riding). It looks like a riding arena. Maybe it belongs to a iding centre, maybe Anglesey Riding Centre (https://www.angleseyridingcentre.co.uk/). In OSM riding arenas are usually tagged with leisure=pitch + sport=equestrian.
See also:
https://wiki.openstreetmap.org/wiki/How_to_map_a#Riding_centre_(equestrian)
https://www.openstreetmap.org/way/260655662 (example)

