Crossword Genius

Having left Billy out, be smugly exultant (5)

Ross

I believe the answer is:

gloat

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'smugly exultant' is the definition.
I can't tell whether this defines the answer.

'having left billy out' is the wordplay.
'having left' becomes 'l' (I can't explain this - if you can you should give a lot more credence to this answer).
'billy' becomes 'goat'.
'out' indicates putting letters inside.
'l' going inside 'goat' is 'GLOAT'.

'be' is the link.

Can you help me to learn more?

(Other definitions for gloat that I've seen before include "Exult maliciously" , "Take malicious satisfaction" , "Express triumphant self-satisfaction" , "Be full of malicious delight" , "Look triumphant" .)

I've seen this clue in the Evening Standard.
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