Long time in that Midwest state (5)
I believe the answer is:
yonks
'long time' is the definition.
(yonks can informally mean many years)
'that midwest state' is the wordplay.
'that' becomes 'yon' (archaic term meaning 'that').
'midwest state' becomes 'KS' (US abbreviation for Kansas).
'yon'+'ks'='YONKS'
'in' is the link.
(Other definitions for yonks that I've seen before include "Ages (informal)" , "Ages (colloq.)" , "Slang for a long time, ages" , "Long time (informal)" , "Donkey's years!" .)