50 per cent left with room to fill grid (7)

I believe the answer is:

lattice

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'fill grid' is the definition.
'lattice' can be an answer for 'grid' (I've seen this before). I am not sure about the 'fill' bit.

'50 per cent left with room' is the wordplay.
'50 per cent' means to take half the letters.
'with' is an insertion indicator.
'room' becomes 'attic' (type of room).
'left' with half the letters taken is 'le'.
'le' going around 'attic' is 'LATTICE'.

'to' is the link.

Can you help me to learn more?

(Other definitions for lattice that I've seen before include "Openwork structure" , "Regular atomic structure" , "Framework of crossed bars as in windows" , "Regular arrangement" , "Sort of window" .)

I've seen this clue in The Times and The Sunday Times.

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