The most common and most likely answer to this crossword clue is the 7 letter word ALASKAN
I've seen this crossword clue in The Sunday Telegraph
A
L
A
S
K
A
N
More clues leading to the result ALASKAN
- Statesman is part of cabal; ask anyone
- American boy carrying request
- Statesman unfortunately cut philosopher short
- Statesman unfortunately known as “Nye”, originally
- Sugar-coated question for statesman?
- A woman may sound in a state
- Sadly, inn’s not hot, in an often frozen state?
- In hospital, ask a nurse, a native of Juneau?
- Person in isolated state, unfortunately — then another, briefly
- A large demand put on an American separated from others
Buddy explains!

The straight part
We know that "Person in isolated state" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case person in isolated state = alaskan.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.