Panic gripping Conservative — that’s rare! (6)
I believe the answer is:
scarce
'rare' is the definition.
(similar in meaning)
'panic gripping conservative' is the wordplay.
'panic' becomes 'scare' (synonyms).
'gripping' means one lot of letters goes inside another (inserted letters are gripped).
'conservative' becomes 'C' (UK political abbreviation).
'scare' going around 'c' is 'SCARCE'.
'that's' is the link.
(Other definitions for scarce that I've seen before include "Deficient in quantity" , "Wanting" , "Hard to get" , "Falling short of demand" , "Scant, meagre" .)