Pitch in with barrel-maker at one end (2-7)

I believe the answer is:

co-operate

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'pitch in' is the definition.
I know nothing about this answer so I can't tell whether this works.

'barrel-maker at one end' is the wordplay.
'barrel maker' becomes 'cooper' (synonyms).
'end' suggests the final letters.
The final letter of 'one' is 'e'.
'cooper'+'at'+'e'='CO-OPERATE'

'with' acts as a link.

Can you help me to learn more?

(Another definition for co-operate that I've seen is " Work together".)

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

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