Task under second in command’s oversight (8)
I believe the answer is:
omission
'oversight' is the definition.
(omission is a kind of oversight)
'task under second in command's' is the wordplay.
'task' becomes 'mission' (I've seen this before).
'under' says to put letters next to each other.
'second in command's' becomes 'o' (ind letter of 'command').
'mission' after 'o' is 'OMISSION'.
(Other definitions for omission that I've seen before include "Leaving-out, oversight" , "It may create space" , "task not done" , "Gap" , "Exclusion" .)