Secret assignment for a lullaby singer? (4-4,3)

I believe the answer is:

hush-hush job

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'a lullaby singer?' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.

'secret assignment' is the wordplay.
'secret' becomes 'hush-hush' (synonyms).
'assignment' becomes 'job' (I've seen this in another clue).
'hushhush'+'job'='HUSH-HUSH JOB'

'for' is the link.

Can you help me to learn more?

I've seen this clue in The Globe and Mail.

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