Crossword Genius

Bishop with eastern monarch for pint (4)

Ross

I believe the answer is:

beer

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

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

'bishop with eastern monarch' is the wordplay.
I cannot quite understand how this works, but
'bishop' could be 'b' (abbreviation for bishop in chess) and 'b' is located in the answer.
'eastern' could be 'e' and 'e' is present in the answer.
'monarch' could be 'er' (abbreviation for Elizabeth Regina, British Queen) and 'er' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

'for' acts as a link.

Can you help me to learn more?

(Other definitions for beer that I've seen before include "See 4 down" , "pint" , "It may be 13 across-ed!" , "Fermented malt and hops" , "Drink with a head" .)

I've seen this clue in The Sun.
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