Hint from student: stick around (4)
I believe the answer is:
clue
'hint' is the definition.
(I know that hint can be written as clue)
'student stick around' is the wordplay.
'student' becomes 'l' (as in L-plates for learner drivers).
'stick' becomes 'cue' (I've seen this before).
'around' means one lot of letters goes inside another.
'l' put within 'cue' is 'CLUE'.
'from' acts as a link.
(Other definitions for clue that I've seen before include "Intimation (like this?)" , "Hint to get what this is?" , "Aid to detection" , "Inkling" , "One indicates" .)