"Not out" rhymes with "opposite" (7)
I believe the answer is:
inverse
'opposite' is the definition.
('inverse' can be a synonym of 'opposite')
'not out rhymes' is the wordplay.
'not out' becomes 'in' ('in' is the opposite to 'out').
'rhymes' becomes 'verse' (I've seen this in other clues).
'in'+'verse'='INVERSE'
'with' acts as a link.
(Other definitions for inverse that I've seen before include "A direct opposite" , "Reversed in position like enviers" , "Something the exact opposite of another" , "The exact opposite of enviers" , "Opposite in direction" .)