The most common and most likely answer to this crossword clue is the 5 plus 6 letter word RHODE ISLAND
I've seen this crossword clue in The Times
R
H
O
D
E
I
S
L
A
N
D
More clues leading to the result RHODE ISLAND
- I, in part of Greece, put down state
- State that would briefly provide religious instruction?
- Doctor Arnold hides in state
- Run hard, followed by mutated aliens in unusual state
- Transformation of older Danish state
- State Street I secure for the lying state?
- Donald’s heir disturbed one U.S. state
- Revolution in older Danish state
Buddy explains!

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