Slog away at the fourth estate, working ... (5,2)
I believe the answer is:
press on
'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" .)