A rival I once sent off for conscription (8,7)
I believe the answer is:
national service
'conscription' is the definition.
(I've seen this before)
'a rival i once sent off' is the wordplay.
'off' is an anagram indicator.
'a'+'rival'+'i'+'once'+'sent'='arivalioncesent'
'arivalioncesent' with letters rearranged gives 'NATIONAL SERVICE'.
'for' is the link.
(Other definitions for national service that I've seen before include "Period of peacetime conscription" , "In a period with the military" , "Period of compulsory conscription" , "Compulsory period in the forces" , "What conscripts had to do" .)