End of quarrel as leader of school leaves hospital (9)

I believe the answer is:
arrowhead
'end' is the definition.
(arrowhead is a kind of end)
'quarrel as leader of school leaves hospital' is the wordplay.
I cannot really see how this works, but
'quarrel' could be 'arrow' (I've seen this before) and 'arrow' is located in the answer.
'leader' could be 'head' (head is a kind of leader) and 'head' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'of' is the link.
Can you help me to learn more?
(Other definitions for arrowhead that I've seen before include "Point to a weapon" , "A suitable end for weapon" , "Water plant" , "Tip of an old projectile" .)
