State Cook discovered circumnavigating Hawaii (4)
I believe the answer is:
ohio
'state' is the definition.
(Ohio is an example)
'cook discovered circumnavigating hawaii' is the wordplay.
'discovered' says to take the centre (dis-covered - outer letters removed).
'circumnavigating' is an insertion indicator.
'hawaii' becomes 'HI' (US postal abbreviation).
The centre of 'cook' is 'oo'.
'oo' enclosing 'hi' is 'OHIO'.
(Other definitions for ohio that I've seen before include "One of the American states" , "Midwestern US state and river" , "American river" , "US state, capital Columbus" , "part of the Midwest!" .)