Initial advantage given in race that reads badly (4,5)
I believe the answer is:
head start
'initial advantage given in race' is the definition.
(advantage at the start of a race)
'that reads badly' is the wordplay.
'badly' indicates an anagram.
'that'+'reads'='thatreads'
'thatreads' is an anagram of 'HEAD START'.
(Other definitions for head start that I've seen before include "An early advantage for the star ad" , "'The advantage of beginning ahead of others (4,5)'" , "Substantial initial advantage" , "Boost?" , "A good beginning using one's loaf" .)