Cautiously cunning about my leaving the army (6)
I believe the answer is:
warily
'cautiously' is the definition.
(I've seen this in another clue)
'cunning about my leaving the army' is the wordplay.
'cunning' becomes 'wily' (synonyms).
'about' indicates putting letters inside.
'leaving' suggests deleting specific letters.
'army' with 'my' taken out is 'ar'.
'wily' placed around 'ar' is 'WARILY'.
(Other definitions for warily that I've seen before include "In a cautious manner" , "With circumspection" , "with caution!" .)