Push discontented hero to give them the sack (7)

I believe the answer is:

heaveho

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'give them the sack' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'push discontented hero' is the wordplay.
'push' becomes 'heave' (I can't justify this - if you can you should believe this answer much more).
'discontented' suggests removing the centre (the word's contents are removed).
'hero' with its centre removed is 'ho'.
'heave'+'ho'='HEAVEHO'

'to' acts as a link.

Can you help me to learn more?

(Another definition for heaveho that I've seen is " dismissal".)

I've seen this clue in The Irish Times.

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