Soon, apparently, Ann will be out of circulation (4)
I believe the answer is:
anon
'soon' is the definition.
(synonyms)
'will be out of circulation' is the wordplay.
'will' says to put letters next to each other (I've seen this in other clues).
'be' becomes 'am'.
'out of' means to remove the last letter (I've seen 'out' mean this).
'circulation' becomes 'non' (I can't explain this - if you can you should give a lot more credence to this answer).
'am' with its final letter taken off is 'a'.
'a'+'non' is 'ANON'.
'apparently ann' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
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" .)