Crossword Genius

A burger, but hold the filling - Bluebird's full (5)

Ross

I believe the answer is:

abrim

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'a burger' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'hold the filling bluebird's full' is the wordplay.
'hold' becomes 'gap'.
'the filling' indicates the central letters (the letters which fill the word).
'bluebird's full' becomes 'brim' (I can't justify this - if you can you should believe this answer much more).
The central letter of 'gap' is 'a'.
'a'+'brim'='ABRIM'

'but' is the link.

Can you help me to learn more?

(Other definitions for abrim that I've seen before include "Completely full" , "Spilling over" .)

I've seen this clue in The Independent.
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