Unwell in old island state (8)
I believe the answer is:
illinois
'state' is the definition.
(I know that Illinois is a state)
'unwell in old island' is the wordplay.
'unwell' becomes 'ill' (similar in meaning).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'island' becomes 'is' (abbreviation).
'ill'+'in'+'o'+'is'='ILLINOIS'
(Other definitions for illinois that I've seen before include "The Prairie State" , "Springfield is the US capital" , "Oil is nil, strangely, in this state" , "Chicago's state" , "Chicago state" .)