Crossword Genius

A coach, but one goes on foot (7)

Ross

I believe the answer is:

trainer

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'foot' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Perhaps you can see an association between them that I can't see?

'a coach but one goes on' is the wordplay.
'a coach' becomes 'train' (both can mean to instruct a sportsperson).
'but one goes' becomes 'er' (I am not sure about this - if you are sure you should believe this answer much more).
'on' says to put letters next to each other.
'train'+'er'='TRAINER'

Can you help me to learn more?

(Other definitions for trainer that I've seen before include "Sports instructor" , "Sports coach" , "Terrain (anag.)" , "Plimsoll or sneaker" , "Soft shoe; simulator" .)

I've seen this clue in The Daily Express.
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