Pie demolished with greed? It runs in the family! (8)

I believe the answer is:

pedigree

'it runs in the family' is the definition.
(pedigree is someone's lineage or family)

'pie demolished with greed?' is the wordplay.
'demolished with' is an anagram indicator.
'pie' anagrammed with 'greed' makes 'PEDIGREE'.

(Other definitions for pedigree that I've seen before include "Pure lineage" , "Lineage of purebred animal" , "Lineage of thoroughbred" , "Stock" , "(Pure) ancestry" .)

I've seen this clue in The Times.

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