Criticises but keeps a nanny? (3,1,2,2)

I believe the answer is:

has a go at

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'criticises' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'keeps a nanny?' is the wordplay.
'keeps' becomes 'has' (keep can mean to have or possess).
'nanny?' becomes 'goat' (nanny is a female goat).
'has'+'a'+'goat'='HAS A GO AT'

'but' is the link.

Can you help me to learn more?

(Another definition for has a go at that I've seen is " pans".)

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

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