Push hard on some media (5)

I believe the answer is:

press

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This clue could be a double definition.

'push hard' is the first definition.
'press' can be an answer for 'push' (press can mean to force or push). I'm unsure of the 'hard' bit.

'some media' is the second definition.
(the press is part of the media)

'on' is the link.

Can you help me to learn more?

(Other definitions for press that I've seen before include "publicity" , "Reporters" , "Urge strongly" , "part of the media" , "Crowd - papers" .)

I've seen this clue in the Sydney Morning Herald.

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