Left, perhaps, though each is on the right (3)
I believe the answer is:
ear
'left' is the definition.
The answer and definition can be both body parts as well as being singular nouns.
Perhaps you can see a link between them that I can't see?
'though each is on the right' is the wordplay.
'though each' becomes 'ea' (abbreviation. I am not sure about the 'though' bit.).
'is on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'the right' becomes 'r' (abbreviation).
'ea'+'r'='EAR'
'perhaps' acts as a link.
Can you help me to learn more?
(Other definitions for ear that I've seen before include "willingness to listen" , "Seed-bearing spike" , "Seed container" , "Discernment musicians need" , "Listener in the cornfield" .)