Greeting a student with old laugh (5)
I believe the answer is:
aloha
'greeting' is the definition.
(I've seen this before)
'a student with old laugh' is the wordplay.
'student' becomes 'L' (as in L-plates for learner drivers).
'with' means one lot of letters go next to another.
'old' becomes 'o' (abbreviation).
'laugh' becomes 'ha'.
'a'+'l'+'o'+'ha'='ALOHA'
(Other definitions for aloha that I've seen before include "greeting in Oahu" , "Hawaiian farewell" , "Hawaiian "ciao"" , "Hello from Honolulu?" , "Hi! in Honolulu" .)