Led, having heard a shot in race (11)
I believe the answer is:
spearheaded
'led' is the definition.
(spearheading is a kind of leading)
'heard a shot in race' is the wordplay.
'shot' is an anagram indicator.
'in' is an insertion indicator.
'race' becomes 'speed' ('speed' can be a synonym of 'race'**).
'heard'+'a'='hearda'
'hearda' is an anagram of 'arhead'.
'arhead' inserted into 'speed' is 'SPEARHEADED'.
'having' acts as a link.
(Other definitions for spearheaded that I've seen before include "Pioneered" , "Led" .)