Teach gloomy poet to grasp piece from Eliot (10)

I believe the answer is:

blackbeard

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'teach' is the definition.
(blackbeard was edward teach)

'gloomy poet to grasp piece from eliot' is the wordplay.
I cannot really see how this works, but
'gloomy' could be 'black' (I've seen this before) and 'black' is located in the answer.
'piece' could be 'beard' (beard is a kind of piece) and 'beard' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...

Can you help me to learn more?

(Another definition for blackbeard that I've seen is " Pirate".)

I've seen this clue in The Times and The Sunday Times.

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