Crossword Genius

Eagerly obtain drink put in dessert from the East (4,2)

Ross

I believe the answer is:

drum up

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'eagerly obtain' is the definition.
I can't judge whether this definition defines the answer.

'drink put in dessert from the east' is the wordplay.
'drink put' becomes 'mur' (I can't explain this - if you can you should believe this answer much more).
'in' means one lot of letters goes inside another.
'dessert' becomes 'pud' (pud is a kind of dessert).
'from the east' says the letters should be written in reverse.
'mur' inserted inside 'pud' is 'pumurd'.
'pumurd' in reverse letter order is 'DRUM UP'.

Can you help me to learn more?

(Other definitions for drum up that I've seen before include "Try to get (something) by canvassing" , "To attract" , "Obtain through vigorous effort - and percussion?" , "Attempt to obtain (support)" , "Attempt to get support by canvassing" .)

I've seen this clue in The Independent.
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