Crossword Genius

Hawking lecture's audience will do so upon arrival (13)

Ross

I believe the answer is:

expectoration

'hawking' is the definition.
(both can mean clearing one's throat)

'lecture's audience will do so upon arrival' is the wordplay.
I cannot really understand how this works, but
'upon' could be 'on' (I've seen this in another clue) and 'on' is located in the answer.
This may be the basis of the clue (or it may be nonsense).

I've seen this clue in The Times.
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