Solitary person - one between left and right (5)
I believe the answer is:
loner
'solitary person' is the definition.
(lonely person)
'one between left and right' is the wordplay.
'between' is an insertion indicator.
'left and right' becomes 'LR' (abbreviations for left and right).
'one' going into 'lr' is 'LONER'.
(Other definitions for loner that I've seen before include "Non-conformist" , "One preferring to act individually" , "Solitary person" , "One shunning society" , "One liking solitude" .)