Acknowledge wrong record in a balance (9)
I believe the answer is:
apologise
'acknowledge wrong' is the definition.
(to apologise is to acknowledge you were wrong)
'record in a balance' is the wordplay.
'record' becomes 'log' (log is a kind of record).
'in' means one lot of letters goes inside another.
'balance' becomes 'poise' (synonyms).
'a'+'poise'='apoise'
'log' placed within 'apoise' is 'APOLOGISE'.
(Other definitions for apologise that I've seen before include "Say sorry, my mistake" , "Recognise fault" , "Ask forgiveness" , "Say sorry, my fault" , "put things straight" .)