Kind of meal done bit by bit (5)

I believe the answer is:

piece

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'bit' is the definition.
(I know that bit can be written as piece)

I don't understand the remainder of the clue.

(Other definitions for piece that I've seen before include "Bishop, for one" , "one of eight once ready for the Spanish?" , "Fragment" , "rook, perhaps" , "One part of a whole" .)

I've seen this clue in The Irish Independent.

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