Improve on high graduate gets with drug (7)

I believe the answer is:

upgrade

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'improve' is the definition.
(I've seen this before)

I can't explain the rest of the clue.

(Other definitions for upgrade that I've seen before include "'Improve, travel status perhaps (7)'" , "Bonus for plane passenger" , "Drug ape to improve" , "advance" , "Improve, enhance" .)

I've seen this clue in The Guardian.

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