One way, on a horse or marching (8)
I believe the answer is:
striding
'marching' is the definition.
('stride' can be a synonym of 'march')
'one way on a horse' is the wordplay.
'one way' becomes 'st' (abbreviation for street).
'on a horse' becomes 'riding' (I've seen this before).
'st'+'riding'='STRIDING'
'or' acts as a link.
(Other definitions for striding that I've seen before include "Walking with long steps" , "edge of the Lake District" , "Stepping out" .)