Wife no longer covered bust, I admitted (8)
I believe the answer is:
divorcee
'wife no longer' is the definition.
I can't judge whether this definition defines the answer.
'covered bust i admitted' is the wordplay.
'bust' indicates anagramming the letters.
'admitted' is an insertion indicator.
'covered' with letters rearranged gives 'dvorcee'.
'dvorcee' going around 'i' is 'DIVORCEE'.
Can you help me to learn more?
(Other definitions for divorcee that I've seen before include "Legally separated person" , "One's marriage has been dissolved" , "Woman with dissolved marriage" , "Legally separated woman" , "List of faults" .)