Southern concern about cold is rare (6)
I believe the answer is:
scarce
'rare' is the definition.
('scarce' can be similar in meaning to 'rare')
'southern concern about cold' is the wordplay.
'southern' becomes 's' (abbreviation).
'concern' becomes 'care' ('care' can be a synonym of 'concern').
'about' is an insertion indicator.
'cold' becomes 'c' (eg on taps).
'care' going around 'c' is 'carce'.
's'+'carce'='SCARCE'
'is' is the link.
(Other definitions for scarce that I've seen before include "Deficient in quantity" , "Wanting" , "Common? Definitely not" , "Insufficient to meet demand" , "Hard to get" .)