Very cold graduate with lieutenant in charge (6)
I believe the answer is:
baltic
'very cold' is the definition.
(baltic can informally mean very cold)
'graduate with lieutenant in charge' is the wordplay.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'with' is a charade indicator (letters next to each other).
'lieutenant' becomes 'lt' (abbreviation for lieutenant).
'in charge' becomes 'ic' (abbreviation for 'in charge').
'ba'+'lt'+'ic'='BALTIC'
(Other definitions for baltic that I've seen before include "Nearly land-locked sea of Scandinavia" , "Near land-locked sea of Scandinavia" , "Cab lit up the sea" , "cold waters" , "Scandinavian sea" .)