Measure following clean-up operation in American state (10)
I believe the answer is:
washington
'american state' is the definition.
(Washington is an example)
'measure following clean-up operation' is the wordplay.
'measure' becomes 'ton' (ton is a kind of measure).
'following' means one lot of letters go next to another.
'clean-up operation' becomes 'washing' (washing is a process of cleaning up).
'ton' after 'washing' is 'WASHINGTON'.
'in' acts as a link.
(Other definitions for washington that I've seen before include "Old president" , "US capital" , "United States capital" , "Seattle's state" , "NW US state" .)