Perhaps time spent working with arms race to maintain (8,7)
I believe the answer is:
national service
'perhaps time spent working with arms' is the definition.
I can't judge whether this defines the answer.
'race to maintain' is the wordplay.
'race' becomes 'national' (horse race the Grand National).
'to maintain' becomes 'service' (I am not sure about this - if you are sure you should believe this answer much more).
'national'+'service'='NATIONAL SERVICE'
Can you help me to learn more?
(Other definitions for national service that I've seen before include "Compulsory period in the forces" , "In a period with the military" , "Period of compulsory conscription" , "Period of peacetime conscription" , "What conscripts had to do" .)