Director of public school in East End (5)
I believe the answer is:
arrow
'director' is the definition.
(something that directs e.g. on a sign)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for arrow that I've seen before include "Mark to indicate direction" , "What's shot from a bow" , "Weapon from bow" , "Projectile from bow" , "Archery projectile" .)