Express one’s regret at fault (8)
I believe the answer is:
'express' is the definition.
'one's regret at fault' is the wordplay.
I cannot really understand how this works, but
'one's' could be 'is' (Roman numeral) and 'is' is found in the answer.
an anagram of 'regret' is 'regter' which is within the left over letters.
This accounts for all the letters.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for register that I've seen before include "Annals", "Make an impression: sign on", "Index", "New arrival at hotel will", "Written record of names, etc".)