Make mistake with mission (6)
I believe the answer is:
Here is my best explanation:
'mission' is the definition.
(I've seen this before)
'make mistake with' is the subsidiary indication.
'make mistake' becomes 'err' (I've seen this before).
'with' becomes 'and'.
(Other definitions for errand that I've seen before include "Short trip to perform required task", "Chore", "Ran red (anag)", "A short journey to deliver orget goods", "Mission (often run)", "Mission usually for others", "Short trip to do a job", "Trip for small task", "Short journey to get or carry message" and "Journey to deliver message etc".)