Crossword Genius

With the current drink, master gets hammered (10)

Ross

I believe the answer is:

downstream

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

'with the current' is the definition.
(I've seen this before)

'drink master gets hammered' is the wordplay.
I cannot really understand how this works, but
'drink' could be 'down' (to down something can mean to drink it quickly) and 'down' is found within the answer.
an anagram of 'master' is 'stream' which is located in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for downstream that I've seen before include "Further along in the flow" , "With the current" , "direction?" .)

I've seen this clue in The Guardian.
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