Wanders about with notice outside Grammar School (4)

I believe the answer is:

gads

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'wanders about' is the definition.
(I've seen this in another clue)

'with notice outside grammar school' is the wordplay.
'with' indicates putting letters inside.
'notice outside' becomes 'ad' (both can mean an advertisement. I am not sure about the 'outside' bit.).
'grammar school' becomes 'GS' (abbreviation for grammar school).
'ad' put inside 'gs' is 'GADS'.

Can you help me to learn more?

(Another definition for gads that I've seen is " Saunters".)

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

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