Publicity about star horse not very good? (5)
I believe the answer is:
pacer
'horse not very good?' is the definition.
(horse bred for pacing)
'publicity about star' is the wordplay.
'publicity' becomes 'pr'.
'about' indicates putting letters inside.
'star' becomes 'ace' ('ace' can be a synonym of 'star').
'pr' going around 'ace' is 'PACER'.
(Other definitions for pacer that I've seen before include "Competitor" , "One who sets the running speed; horse" , "early race leader?" , "Racehorse" , "setting the rate" .)