Left out of greeting that goes over saint's head? (4)
I believe the answer is:
halo
'that goes over saint's head?' is the definition.
(saints are often depicted with haloes)
'left out of greeting' is the wordplay.
'left' becomes 'l' (common abbreviation).
'out of' is a deletion indicator.
'greeting' becomes 'hallo' (alternative to hello).
'hallo' with 'l' removed is 'HALO'.
(Other definitions for halo that I've seen before include "Symbol of sainthood" , "Saint's headlight?" , "Saintly ring" , "Sign of a saint" , "Band of light" .)