Crossword Genius

Ineptitude from eg Macron briefly meeting Blair (9)

Ross

I believe the answer is:

gaucherie

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'ineptitude' is the definition.
(thesaurus)

'briefly meeting blair' is the wordplay.
'briefly' becomes 'gau' (I can't explain this - if you can you should give a lot more credence to this answer).
'meeting' says to put letters next to each other.
'blair' becomes 'Cherie' (Cherie Blair, wife of Tony Blair).
'gau'+'cherie'='GAUCHERIE'

'from eg macron' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for gaucherie that I've seen before include "Slip" , "Awkwardness" , "Faux pas" , "clumsiness" , "clumsy behaviour" .)

I've seen this clue in The Guardian.
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