Spoke about drink after one began (10)

I believe the answer is:

originated

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'one began' is the definition.
(to originate something is to begin it)

'spoke about drink' is the wordplay.
'spoke' becomes 'orated' (to orate is to give a speech).
'about' means one lot of letters goes inside another.
'drink' becomes 'igin' (I can't explain this - if you can you should believe this answer much more).
'orated' going around 'igin' is 'ORIGINATED'.

'after' is the link.

Can you help me to learn more?

(Another definition for originated that I've seen is " Started".)

I've seen this clue in The Guardian.

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