Authorisation for each assignment (10)
I believe the answer is:
permission
'authorisation' is the definition.
(permission is a kind of authorisation)
'each assignment' is the wordplay.
'each' becomes 'per'.
'assignment' becomes 'mission' (mission is a kind of assignment).
'per'+'mission'='PERMISSION'
'for' is the link.
(Other definitions for permission that I've seen before include "Leave" , "Consent, authorisation" , "Visa, eg" , "Allowance" , "Green light" .)