The weariness of military duty (7)
I believe the answer is:
fatigue
This might be a double definition.
'the weariness' is the first definition.
('fatigue' can be a synonym of 'weariness')
'military duty' is the second definition.
'fatigue' can be an answer for 'duty' (fatigue duty is a kind of duty). I am unsure of the 'military' bit.
'of' acts as a link.
Can you help me to learn more?
(Other definitions for fatigue that I've seen before include "Tire" , "Tommy's punishment" , "Weariness from labour" , "Chronic symptom" , "weary" .)