Race the old lady runs with unusual hat on (8)
I believe the answer is:
marathon
'race' is the definition.
(marathon is a kind of race)
'the old lady runs with unusual hat on' is the wordplay.
'the old lady' becomes 'ma'.
'runs' becomes 'r' (cricket abbreviation).
'with' means one lot of letters go next to another.
'unusual' indicates an anagram.
'hat' anagrammed gives 'ath'.
'ma'+'r'+'ath'+'on'='MARATHON'
(Other definitions for marathon that I've seen before include "Footrace of approx 26 miles" , "Race; battle" , "26-mile foot race" , "Long-distance running event" , "Olympic event" .)