Girls get schooled outside home? That's brilliant! (10)

I believe the answer is:

glistering

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'brilliant' is the definition.
Both the answer and definition are adjectives. Maybe they are linked in a way I don't understand?

'girls get schooled outside home?' is the wordplay.
'girls' becomes 'gg' (an abbreviation for girl written twice).
'get' means one lot of letters goes inside another.
'schooled outside' becomes 'lister' (I can't explain this - if you can you should believe this answer much more).
'home?' becomes 'in' ('he's home' can mean 'he's in').
'lister'+'in'='listerin'
'gg' placed around 'listerin' is 'GLISTERING'.

'that's' is the link.

Can you help me to learn more?

I've seen this clue in The Independent.

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