What Haig had? Nasty ordeal, first of many (7)

I believe the answer is:

earldom

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'what haig had?' is the definition.
I can't judge whether this definition defines the answer.

'nasty ordeal first of many' is the wordplay.
'nasty' indicates anagramming the letters.
'first of' says to take the initial letters.
The first letter of 'many' is 'm'.
'ordeal' anagrammed gives 'earldo'.
'earldo'+'m'='EARLDOM'

Can you help me to learn more?

(Other definitions for earldom that I've seen before include "Noble rank" , "Aristocratic domain above a viscountcy but below a marquessate" , "Units" , "Domain of a mid-ranking peer" , "Norfolk or Wessex, for example" .)

I've seen this clue in The Telegraph.

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