Kelvin joining an elite army unit in state (6)
I believe the answer is:
kansas
'state' is the definition.
(I know that Kansas is American state)
'kelvin joining an elite army unit' is the wordplay.
'kelvin' becomes 'K' (abbreviation for the unit of temperature).
'joining' is a charade indicator (letters next to each other).
'elite army unit' becomes 'SAS' (short for Special Air Service).
'k'+'an'+'sas'='KANSAS'
'in' is the link.
(Other definitions for kansas that I've seen before include "''Toto, I've a feeling we're not in ... anymore'' (Dorothy in Wizard of Oz)" , "seen about in region round Topeka" , "Central US state" , "State of central USA" , "US state, capital Topeka" .)