More sensitive, overturned Duke’s compensation (6)

I believe the answer is:

reward

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'compensation' is the definition.
(I've seen this in another clue)

I don't understand how the remainder of the clue works.

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(Other definitions for reward that I've seen before include "Deserved prize" , "Recompense, remunerate" , "Bounty; recompense" , "Present given to mark service or good deed" , "Profit, return" .)

I've seen this clue in The Times.

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