Blood sport, day one: endless avarice (8)
I believe the answer is:
pedigree
'blood' is the definition.
(I know that blood can be written as pedigree)
'sport day one endless avarice' is the wordplay.
'sport' becomes 'pe' (physical education).
'day' becomes 'd' (abbreviation for day).
'one' becomes 'i' (Roman numeral).
'endless' means to remove the last letter.
'avarice' becomes 'greed' (synonyms).
'greed' with its final letter removed is 'gree'.
'pe'+'d'+'i'+'gree'='PEDIGREE'
(Other definitions for pedigree that I've seen before include "Record of descent" , "Stock" , "What a mongrel doesn't have" , "(Pure) ancestry" , "Of animals, recorded line of descent" .)