Soldiers don’t initially get better (4)
I believe the answer is:
mend
'get better' is the definition.
('mend' can be a synonym of 'get better')
'soldiers don't initially' is the wordplay.
'soldiers' becomes 'men' (I've seen this before).
'initially' says to take the initial letters.
The initial letter of 'dont' is 'd'.
'men'+'d'='MEND'
(Other definitions for mend that I've seen before include "Return to health; repair" , "'Restore, fix (4)'" , "Fix, repair" , "Heal" , "Make improvements" .)