Crossword Genius

Pupil covered in lard entirely (4)

Ross

I believe the answer is:

flat

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'entirely' is the definition.
Both the answer and definition are adverbs. Maybe they are linked in a way I don't understand?

'pupil covered in lard' is the wordplay.
'pupil' becomes 'l'.
'covered in' means one lot of letters goes inside another.
'lard' becomes 'fat' (I can't justify this - if you can you should give a lot more credence to this answer).
'l' going into 'fat' is 'FLAT'.

Can you help me to learn more?

(Other definitions for flat that I've seen before include "Level - below the natural note" , "No longer charged" , "Quarters - punctured - smooth" , "Apartment - on the level" , "razed to the ground, having had blow-out" .)

I've seen this clue in The Independent.
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