Bring over sharp tool and cut frame to be precise (5)

I believe the answer is:

exact

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'precise' is the definition.
(I know that precise can be written as exact)

'bring over sharp tool and cut frame' is the wordplay.
'bring over' shows that the letters should be reversed in order (I've seen 'brought over' mean this).
'sharp tool' becomes 'axe' (axe is a kind of tool. I am not sure about the 'sharp' bit.).
'and' means one lot of letters go next to another.
'frame' suggests removing the centre.
'cut' with its middle taken out is 'ct'.
'axe' written backwards gives 'exa'.
'exa'+'ct'='EXACT'

'to be' acts as a link.

Can you help me to learn more?

(Other definitions for exact that I've seen before include "Precise; extort" , "Precise and strictly correct" , "totally accurate" , "Finished" , "Precise, accurate" .)

I've seen this clue in The Irish Times.

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