Rival, once neat, is upset with conscription (8,7)
I believe the answer is:
national service
'conscription' is the definition.
(I've seen this before)
'rival once neat is upset' is the wordplay.
'upset' indicates anagramming the letters.
'rival'+'once'+'neat'+'is'='rivalonceneatis'
'rivalonceneatis' with letters rearranged gives 'NATIONAL SERVICE'.
'with' acts as a link.
(Other definitions for national service that I've seen before include "In a period with the military" , "Compulsory period in the forces" , "Period of peacetime conscription" , "What conscripts had to do" , "Period of compulsory conscription" .)