Sensitive Conservative regularly dithers about thick-skinned individual (10)
I believe the answer is:
rhinoceros
'thick-skinned individual' is the definition.
(animal with thick skin)
'sensitive conservative regularly dithers about' is the wordplay.
'sensitive' becomes 'sore' (as in a sore wound).
'conservative' becomes 'con' (abbreviation for Conservative).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'about' says the letters should be written backwards.
The alternating letters of 'dithers' are 'ihr'.
'sore'+'con'+'ihr'='soreconihr'
'soreconihr' written backwards gives 'RHINOCEROS'.
(Other definitions for rhinoceros that I've seen before include "Thick-skinned beast" , "Large horned animal" , "Ionesco play" , "Horned ungulate" , "Horny type" .)