Hand over responsibility for the underpass and keep batting (4,3,5)

I believe the answer is:

pass the baton

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'underpass and keep batting' is the definition.
I know nothing about this answer so I can't tell whether this works.

'hand over responsibility for the' is the wordplay.
'hand over' becomes 'pass'.
'responsibility' becomes 'baton' (I can't justify this - if you can you should believe this answer much more).
'for' means one lot of letters go next to another (I've seen this in other clues).
'baton' after 'the' is 'thebaton'.
'pass'+'thebaton'='PASS THE BATON'

Can you help me to learn more?

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

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