Improvement day amongst soldiers after a time (9)
I believe the answer is:
amendment
'improvement' is the definition.
(amendment is a kind of improvement)
'amongst soldiers after a time' is the wordplay.
'amongst' becomes 'amend' (I can't explain this - if you can you should give a lot more credence to this answer).
'soldiers' becomes 'men' (I've seen this before).
'after' says to put letters next to each other.
'a time' becomes 't' (abbreviation).
'amend'+'men'+'t'='AMENDMENT'
'day' acts as a link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for amendment that I've seen before include "a bit of a change!" , "the fifth one benefiting Uncle Sam's defendants?" , "Statement added to or revising a document" , "A qualification" , "change for the better" .)