Crossword Genius

Brew drink in fresh coffee, finally (9)

Ross

I believe the answer is:

percolate

I'm a little stuck... Click here to teach me more about this clue!

'brew' is the definition.
(thesaurus)

'drink in fresh coffee finally' is the wordplay.
I cannot quite see how this works, but
'drink' could be 'cola' (cola is a kind of drink) and 'cola' is found in the answer.
'fresh' could be 'pert' (I've seen this in another clue) and 'pert' is found within the remaining letters.
A single letter 'e' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for percolate that I've seen before include "Filter - to replace (anag)" , "Sift gradually through clear poet" , "Pass through fine openings, like coffee say" , "Penetrate gradually" , "Strain" .)

I've seen this clue in The Guardian.
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