Holy man going on horseback or walking (8)
I believe the answer is:
striding
'walking' is the definition.
(striding is a kind of walking)
'holy man going on' is the wordplay.
'holy man' becomes 'st' (abbreviation for saint).
'going' becomes 'riding' (riding is a kind of going).
'on' means one lot of letters go next to another.
'st'+'riding'='STRIDING'
'horseback or' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for striding that I've seen before include "Walking with long steps" , "Stepping out" , "edge of the Lake District" .)