Make mistake with mission (6)
I believe the answer is:
errand
'mission' is the definition.
(thesaurus)
'make mistake with' is the wordplay.
'make mistake' becomes 'err' (I've seen this before).
'with' becomes 'and' (I've seen this before).
'err'+'and'='ERRAND'
(Other definitions for errand that I've seen before include "Mission (usually run!)" , "run one" , "A short journey to deliver orget goods" , "Mission usually for others" , "Job usually involving a short trip" .)