Too proud chopping tarragon (8)

I believe the answer is:

arrogant

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'too proud' is the definition.
'arrogant' can be an answer for 'proud' (similar in meaning). I am not sure about the 'too' bit.

'chopping tarragon' is the wordplay.
'chopping' indicates anagramming the letters (I've seen 'chopped' mean this (letters chopped or smashed up)).
'tarragon' is an anagram of 'ARROGANT'.

Can you help me to learn more?

(Other definitions for arrogant that I've seen before include "Proud and contemptuous" , "Disdainful" , "Over-cocky" , "Cocky" , "Overbearingly proud" .)

I've seen this clue in The Sun.

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