Property of some numbers – remove pairs and one remains (7)
I believe the answer is:
oddness
'property of some numbers remove pairs' is the definition.
I know that 'numbers' relates to this answer.
'one remains' is the wordplay.
'one' becomes 'odd' (I've seen this before).
'remains' becomes 'ness' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'odd'+'ness'='ODDNESS'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for oddness that I've seen before include "Eccentricity" , "Peculiar quality" , "Curious state" , "It isn't even" , "a peculiarity of character" .)