Becomes public knowledge that one’s a gadabout (4,5)

I believe the answer is:

gets round

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'one's a gadabout' is the definition.
I know nothing about this answer so I can't judge whether this works.

'becomes public knowledge' is the wordplay.
'becomes' becomes 'gets' ('get' can be a synonym of 'become').
'public knowledge' becomes 'round' (I can't justify this - if you can you should believe this answer much more).
'gets'+'round'='GETS ROUND'

'that' acts as a link.

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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