Half of the horses run (4)
I believe the answer is:
trot
'run' is the definition.
(trot is a kind of run)
'half of the horses' is the wordplay.
'half of' suggests halving the letters.
'the horses' becomes 'trotters' (trotter is a kind of horse).
'trotters' cut in half is 'TROT'.
(Other definitions for trot that I've seen before include "Move at brisk pace" , "Steady gentle run" , "Move briskly" , "movement of H [TROT]" , "Horse's gait - extreme leftist" .)