Republican greeting flipping angry prisoner -- one has a thick skin (10)
I believe the answer is:
rhinoceros
'one has a thick skin' is the definition.
(I know this)
'republican greeting flipping angry prisoner' is the wordplay.
'republican' becomes 'r' (abbreviation).
'greeting' becomes 'hi' (hi is a kind of greeting).
'flipping' shows that the letters should be reversed in order.
'angry' becomes 'sore' (similar in meaning).
'prisoner' becomes 'con' (abbreviation for 'convict').
'sore'+'con'='sorecon'
'sorecon' back-to-front is 'noceros'.
'r'+'hi'+'noceros'='RHINOCEROS'
(Other definitions for rhinoceros that I've seen before include "Horned creature" , "Thick-skinned beast" , "Native of Africa" , "Horned mammal" , "Endangered animal" .)