Terribly nasty about Conservative being thin (6)
I believe the answer is:
scanty
'being thin' is the definition.
(I've seen this in another clue)
'terribly nasty about conservative' is the wordplay.
'terribly' indicates an anagram.
'about' is an insertion indicator.
'conservative' becomes 'C' (UK political abbreviation).
'nasty' anagrammed gives 'santy'.
'santy' going around 'c' is 'SCANTY'.
(Other definitions for scanty that I've seen before include "Lacking in amplitude or quantity" , "Give (to a good cause)" , "Spare" , "Insufficient in quantity" , "(Of clothing) skimpy" .)