Trainers chase horse and colt all over the place (14)

I believe the answer is:

schoolteachers

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'trainers' is the definition.
The answer and definition can be both people as well as being plural nouns.
Perhaps you can see an association between them that I can't see?

'chase horse and colt all over the place' is the wordplay.
'and' is a charade indicator (letters next to each other).
'all over the place' indicates an anagram.
'chase'+'horse'='chasehorse'
'chasehorse' put after 'colt' is 'coltchasehorse'.
'coltchasehorse' is an anagram of 'SCHOOLTEACHERS'.

Can you help me to learn more?

I've seen this clue in The Guardian.

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