Crossword Genius

Engage in sport or cheat at it (4)

Ross

I believe the answer is:

dope

'engage' is the definition.
Although both the answer and definition are verbs in their base form, I can't see how one could define the other.

'sport or cheat at it' is the wordplay.
I cannot really understand how this works, but
'sport' could be 'pe' (physical education) and 'pe' is found within the answer.
'cheat' could be 'do' and 'do' is found within the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

'in' is the link.

(Other definitions for dope that I've seen before include "Dolt -- drug" , "Informal drug or stupid person" , "One simple" , "Silly type" , "Fool - model aeroplane varnish" .)

I've seen this clue in The Guardian.
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