A hut sadly in a state (4)
I believe the answer is:
utah
'a state' is the definition.
(Utah is an example)
'a hut sadly in' is the wordplay.
'sadly' indicates an anagram.
'in' is an insertion indicator.
'hut' anagrammed gives 'uth'.
'a' placed inside 'uth' is 'UTAH'.
(Other definitions for utah that I've seen before include "American state associated with Mormons and their faith" , "US state, capital Salt Lake City" , "Brigham Young state" , "US state settled by the Mormons" , "The American Morman state" .)