Posh school that fails to open causing quarrel? (5)
I believe the answer is:
arrow
'quarrel?' is the definition.
(quarrel is a kind of arrow)
'posh school that fails to open' is the wordplay.
'posh school' becomes 'harrow' (English private school).
'that fails to open' means to remove the first letter.
'harrow' with its initial letter taken away is 'ARROW'.
'causing' is the link.
(Other definitions for arrow that I've seen before include "Pointed weapon" , "Sharp-tipped missile" , "Missile for bowman" , "marker" , "Type of projectile" .)