It's not up to the laundry to provide capital (10)
I believe the answer is:
washington
'capital' is the definition.
(capital of the USA)
'it's not up to the laundry' is the wordplay.
I cannot really see how this works, but
an anagram of 'not' is 'ton' which is present in the answer.
'laundry' could be 'washing' (I've seen this before) and 'washing' is found in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
'to provide' acts as a link.
Can you help me to learn more?
(Other definitions for washington that I've seen before include "United States capital" , "Irving" , "NW US state" , "American general and president" , "First US president" .)