The most common and most likely answer to this crossword clue is the 8 letter word GEORGIAN
I've seen this crossword clue in The Times
G
E
O
R
G
I
A
N
More clues leading to the result GEORGIAN
- East European and American statesman are going out
- Style of Sheraton built in Atlanta, perhaps
- Former Russian, American or English architecture
- Style of architecture, one from the southern US
- Former Soviet, say, backing one probing agency
- Man briefly joins another person from Atlanta?
- Second point off Bush and Botham, coming from Augusta!
- Architectural style from state on Atlantic
Buddy explains!
The straight part
We know that "East European/American statesman" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case east european/american statesman = georgian.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.