Very emotional leader of Conservatives appearing in absurd hairstyle (10)
I believe the answer is:
hysterical
'very emotional' is the definition.
(hysteria is extreme emotion)
'leader of conservatives appearing in absurd hairstyle' is the wordplay.
'leader of' suggests taking the first letters.
'appearing in' means one lot of letters goes inside another.
'absurd' is an anagram indicator.
The initial letter of 'conservatives' is 'c'.
'hairstyle' anagrammed gives 'hysterial'.
'c' put within 'hysterial' is 'HYSTERICAL'.
(Other definitions for hysterical that I've seen before include "Wildly uncontrolled" , "Wildly funny" , "Emotionally unstable" , "overwrought" , "Extremely funny" .)