Between right and left, each is genuine (4)
I believe the answer is:
real
'is genuine' is the definition.
('real' is associated in meaning with 'genuine')
'between right and left' is the wordplay.
'between right' becomes 'rea' (I can't explain this - if you can you should believe this answer much more).
'and' is a charade indicator (letters next to each other).
'left' becomes 'l' (common abbreviation).
'rea'+'l'='REAL'
'each' acts as a link.
This may not be right. It may belong to another bit of the clue.
(Other definitions for real that I've seen before include "Actual, existing" , "Type of ale" , "Unaffected" , "very American" , "Actually existing" .)