Moderate results from having booster jab study (6)

I believe the answer is:

dampen

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'moderate' is the definition.
(thesaurus)

I don't understand the remainder of the clue.

(Other definitions for dampen that I've seen before include "Make moist (6)" , "Make moist or depress spirits" , "Moisten" , "Make moist or subdued" , "Apply liquid!" .)

I've seen this clue in The Times.

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