The most common and most likely answer to this crossword clue is the 10 letter word WASHINGTON
I've seen this crossword clue in The Times
W
A
S
H
I
N
G
T
O
N
More clues leading to the result WASHINGTON
- Dirty linen not to be written about in seat of government
- US president saw nothing out of place
- Measure following clean-up operation in American state
- Weight put behind domestic chore in US state
- President’s dirty laundry not to be broadcast!
- Nothing was new for this new president
- State of laundry? Not bad
- One in fifty used to be on night shifts
- General oversaw nothing fishy
- State capital
Buddy explains!
The straight part
We know that "seat of government" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case seat of government = washington.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.