Intervene: give drugs to eliminate cold (7)

I believe the answer is:

mediate

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'intervene' is the definition.
(to mediate is to intervene between two parties)

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

Can you help me to learn more?

(Other definitions for mediate that I've seen before include "ie Tamed (anag.)" , "To referee" , "Help settle a dispute" , "Arbitrate between parties in dispute" , "Act between parties to reconcile differences" .)

I've seen this clue in The Sun.

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