Simple air possibly unknown by Arne? Not half (10)
I believe the answer is:
elementary
'simple' is the definition.
('elementary' can be a synonym of 'simple')
'air possibly unknown by arne? not half' is the wordplay.
'air possibly' becomes 'element' (air is a kind of element**).
'unknown' becomes 'y' (algebra).
'by' means one lot of letters go next to another.
'not half' means to take half the letters.
'arne' halved is 'ar'.
'y' after 'ar' is 'ary'.
'element'+'ary'='ELEMENTARY'
(Other definitions for elementary that I've seen before include "Easy" , "Simple, introductory" , "Primary" , "One precursor to 7 [SECONDARY MODERN]" , "Fundamental" .)