Register border between left and right (6)
I believe the answer is:
ledger
'register' is the definition.
(thesaurus)
'border between left and right' is the wordplay.
'border' becomes 'edge' (synonyms).
'between' means one lot of letters goes inside another.
'left and right' becomes 'LR' (abbreviations for left and right).
'edge' going within 'lr' is 'LEDGER'.
(Other definitions for ledger that I've seen before include "Book-keeper's book" , "Elderly resident" , "Heath -, Australian actor" , "Business record book" , "Accounts journal" .)