Make mistake with mission (6)
I believe the answer is:
Here is my best explanation:
'mission' is the definition.
'make mistake with' is the wordplay.
'make mistake' becomes 'err' (I've seen this before).
'with' becomes 'and' (I've seen this before).
(Other definitions for errand that I've seen before include "Job usually involving a short trip", "Native of a former German kingdom", "run one", "purposeful journey", "Short assignment", "Short trip to do a job", "Short journey on behalf of another", "Mission (usually run!)", "Short trip with a mission" and "Commission, task".)