Go astray with mission (6)
I believe the answer is:
errand
'mission' is the definition.
(I've seen this before)
'go astray with' is the wordplay.
'go astray' becomes 'err' (to err is to make an error or go the wrong way).
'with' becomes 'and'.
'err'+'and'='ERRAND'
(Other definitions for errand that I've seen before include "Short journey to carry message for Renard" , "Trip for small task" , "Short journey on behalf of another" , "A little job" , "Delivery/collection trip" .)