PM Heath irate about site for old contest (12)

I believe the answer is:

amphitheatre

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'site for old contest' is the definition.
I can't judge whether this definition defines the answer.

'pm heath irate about' is the wordplay.
'about' is an anagram indicator.
'pm'+'heath'+'irate'='pmheathirate'
'pmheathirate' with letters rearranged gives 'AMPHITHEATRE'.

Can you help me to learn more?

(Other definitions for amphitheatre that I've seen before include "Large oval stadium with tiers of seats" , "Open auditorium" , "Classical performance area" , "Arena; gallery tier" , "Roman tiered arena" .)

I've seen this clue in The Times.

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