Overhaul Descartes for one, reversing axiom (7)
I believe the answer is:
renewal
'overhaul' is the definition.
(an overhaul of something might be a renewal of it)
'descartes for one reversing axiom' is the wordplay.
'descartes' becomes 'Rene Descartes' (as in Rene Descartes the French philosopher).
'for' says to put letters next to each other.
'one reversing' says the letters should be written backwards.
'axiom' becomes 'law' (an axiom is a law or principle).
'law' backwards is 'wal'.
'rene'+'wal'='RENEWAL'
(Other definitions for renewal that I've seen before include "reconditioning" , "Extension of validity" , "Restoration, recovery" , "modernisation?" , "Modernization" .)