Saint has to go on horseback or walk with big steps (6)
I believe the answer is:
stride
'walk with big steps' is the definition.
'stride' can be an answer for 'walk' (stride can mean to walk around). I'm not sure about the 'with big steps' bit.
'saint has to go on horseback' is the wordplay.
'saint' becomes 'st' (abbreviation).
'has' means one lot of letters go next to another.
'to go on horseback' becomes 'ride' (I've seen this before).
'st'+'ride'='STRIDE'
'or' acts as a link.
Can you help me to learn more?
(Other definitions for stride that I've seen before include "use your legs!" , "jazz piano-playing" , "Take a long step" , "A big step forward" , "Step out energetically" .)