Edgar Allen drinks regular weak tea (5)

I believe the answer is:

pekoe

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'tea' is the definition.
(I know that pekoe is a tea)

'edgar allen drinks regular weak' is the wordplay.
'edgar allen' becomes 'poe' (I am not sure about this - if you are sure you should believe this answer much more).
'drinks' indicates putting letters inside (inserted letters are consumed or drunk).
'regular' indicates alternate letters.
The alternate letters of 'weak' are 'ek'.
'poe' placed around 'ek' is 'PEKOE'.

Can you help me to learn more?

(Other definitions for pekoe that I've seen before include "High quality black tea" , "brew" , "Superior grade of black tea" , "Scented black tea" , "High-quality black tea" .)

I've seen this clue in the Sydney Morning Herald.

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