People in Derby perhaps? (4)

I believe the answer is:

race

I'm a little stuck... Click here to teach me more about this clue!

'people in derby' is the definition.
'race' can be an answer for 'derby' (I've seen this in another clue). I am not sure about the 'people in' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for race that I've seen before include "Run - competition" , "Move fast" , "The ... is not to the swift (Bible)" , "Run quickly" , "Run swiftly" .)

I've seen this clue in The Times.

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