Starts to throw out some household rubbish (4)
I believe the answer is:
tosh
'rubbish' is the definition.
(both can mean nonsense)
'starts to throw out some household' is the wordplay.
'starts to' indicates taking the first letters.
The initial letters of 'throw out some household' is 'TOSH'.
(Other definitions for tosh that I've seen before include "Rubbish, nonsense" , "13 [TRIPE]" , "Humbug" , "Hooey" , "Drivel" .)