Bad hairdo -- run out in such a state (5)
I believe the answer is:
idaho
'such a state' is the definition.
(Idaho is an example)
'bad hairdo run out' is the wordplay.
'bad' is an anagram indicator.
'run' becomes 'r' (cricket abbreviation).
'out' is a deletion indicator.
'hairdo' with 'r' taken away is 'haido'.
'haido' anagrammed gives 'IDAHO'.
'in' is the link.
(Other definitions for idaho that I've seen before include "somewhere in the US" , "The Gem State, known for its potatoes" , "US state E. of Oregon" , "North-western US state" , "US state, capital Boise" .)