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Slog away at the fourth estate, working ... (5,2)

Ross

I believe the answer is:

press on

I'm a little stuck... Click here to teach me more about this clue!

'slog away' is the definition.
I can't tell whether this defines the answer.

'at the fourth estate working' is the wordplay.
'at' is a charade indicator (letters next to each other).
'the fourth estate' becomes 'press' (term for the press).
'working' becomes 'on' (on can mean working or activated).
'press'+'on' is 'PRESS ON'.

Can you help me to learn more?

(Other definitions for press on that I've seen before include "Hasten insistently" , "don't stop!" , "Continue (regardless)" , "Persevere doggedly, quickly" , "Continue going forward" .)

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