Following one day in city, in a terrible state (9)
I believe the answer is:
lithuania
'a terrible state' is the definition.
'lithuania' can be an answer for 'state' (I've seen this before). I am not sure about the 'a terrible' bit.
'following one day in city in' is the wordplay.
'following' says to put letters next to each other.
'one' becomes 'li' (I've seen this in other clues).
'day' becomes 'thu' (abbreviation for Thursday).
'in city in' becomes 'ania' (I can't justify this - if you can you should give a lot more credence to this answer).
'li' next to 'thu' is 'lithu'.
'lithu'+'ania'='LITHUANIA'
(Other definitions for lithuania that I've seen before include "republican area" , "Northeast European country" , "land" , "European country, capital Vilnius" , "Baltic state" .)