Give out the centre part of text due for revision (5)

I believe the answer is:

exude

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'give out' is the definition.
(I've seen this before)

'the centre part of text due for revision' is the wordplay.
'the' becomes 'definite article' ('the' is the definite article in English).
'centre' says to take the centre.
'part of text' becomes 'x' (I am not sure about this - if you are sure you should believe this answer much more).
'for revision' is an anagram indicator (I've seen this in other clues).
The middle of 'definitearticle' is 'e'.
'due' with letters rearranged gives 'ude'.
'e'+'x'+'ude'='EXUDE'

Can you help me to learn more?

(Other definitions for exude that I've seen before include "Radiate" , "Discharge (something) slowly" , "Long-legged wader" , "Release" , "Seep" .)

I've seen this clue in The Globe and Mail.

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