Race tyres can burst (8)
I believe the answer is:
ancestry
'race' is the definition.
(thesaurus)
'tyres can burst' is the wordplay.
'burst' indicates anagramming the letters.
'tyres'+'can'='tyrescan'
'tyrescan' anagrammed gives 'ANCESTRY'.
(Other definitions for ancestry that I've seen before include "race" , "Blood line" , "Any crest (anag.)" , "Line of forebears" , "Line of descendants" .)