Doctor is rich but arrogant (9)

I believe the answer is:

hubristic

'arrogant' is the definition.
(thesaurus)

'doctor is rich but' is the wordplay.
'doctor' indicates an anagram.
'is'+'rich'+'but'='isrichbut'
'isrichbut' with letters rearranged gives 'HUBRISTIC'.

(Other definitions for hubristic that I've seen before include "arrogant" , "Excessively proud" .)

I've seen this clue in The Independent.

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