People's champions rushed past to get prize (3,5,5,2)

I believe the answer is:

lay great store by

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'people's champions' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'rushed past to get prize' is the wordplay.
I cannot quite see how this works, but
'rushed' could be 'tore' (to tear around is to rush or run fast) and 'tore' is found in the answer.
'past' could be 'by' (as in years gone by) and 'by' is found within the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Times.

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