Give contrary baronet 'Aeneid' subsection to tidy up (6)

I believe the answer is:

neaten

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'to tidy up' is the definition.
('neaten' can be a synonym of 'tidy up')

'give contrary baronet aeneid subsection' is the wordplay.
'NEATEN' is hidden back-to-front within the letters.
But, I am uncertain how this is indicated.

Can you help me to learn more?

(Other definitions for neaten that I've seen before include "Trim" , "Spruce up" , "set in order" , "Groom" , "Straighten up" .)

I've seen this clue in The Irish Times.

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