Express regret a record is kept by US writer (9)
I believe the answer is:
apologise
'express regret' is the definition.
(I've seen this before)
'a record is kept by us writer' is the wordplay.
'record' becomes 'log' (logging is a kind of recording).
'kept by' is an insertion indicator.
'us writer' becomes 'poe' (writer Edgar Allan Poe).
'log'+'is'='logis'
'logis' placed within 'poe' is 'pologise'.
'a'+'pologise'='APOLOGISE'
(Other definitions for apologise that I've seen before include "Express regret for a wrong (S, not Z)" , "Show regret" , "Recognise fault" , "Ask forgiveness" , "Say sorry, my mistake" .)