Encounter inferior bit of beer, nothing more (4,4)

I believe the answer is:

bump into

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'encounter' is the definition.
(synonyms)

'inferior bit of beer nothing more' is the wordplay.
'inferior bit of' becomes 'bum' (I can't justify this - if you can you should believe this answer much more).
'beer' becomes 'pint'.
'nothing more' becomes 'o' (resembles 0).
'bum'+'pint'+'o'='BUMP INTO'

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(Other definitions for bump into that I've seen before include "Chance upon" , "Happen to meet - ouch!" , "meet, unexpectedly" , "Meet by chance - in collision?" , "Come across unexpectedly" .)

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