No time for chores: big ones are onerous! (4)
I believe the answer is:
asks
'big ones are onerous' is the definition.
(that's a big ask!)
'no time for chores' is the wordplay.
'no' is a deletion indicator.
'time for' becomes 't' (I've seen this in other clues).
'chores' becomes 'tasks' ('task' can be a synonym of 'chore').
'tasks' with 't' taken away is 'ASKS'.
(Other definitions for asks that I've seen before include "Makes an inquiry" , "Poses a question" , "Puts a query" , "Requests information about" , "Enquires; requests" .)