Start of week as the husband's taken out rubbish (5)
I believe the answer is:
waste
'rubbish' is the definition.
(I know that rubbish can be written as waste)
'start of week as the husband's taken' is the wordplay.
'start of' says to take the initial letters.
'the husband's taken' becomes 'te' (I am not sure about this - if you are sure you should believe this answer much more).
The first letter of 'week' is 'w'.
'w'+'as'+'te'='WASTE'
'out' is the link.
Can you help me to learn more?
(Other definitions for waste that I've seen before include "Throw away thoughtlessly" , "Useless leftovers" , "Use carelessly" , "Atrophy" , "Rubbish, barren land" .)