Soon, apparently, Ann will be out of circulation (4)
I believe the answer is:
anon
'soon' is the definition.
(synonyms)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for anon that I've seen before include "Soon; unattributed" , "Soon - nobody knows me" , "Soon; unnamed" , "Of unknown identity, in short" , "In due course" .)