Look for well-groomed missing student (4)
I believe the answer is:
seek
'look for' is the definition.
(synonyms)
'well-groomed missing student' is the wordplay.
'well groomed' becomes 'sleek' (I've seen this in another clue).
'missing' is a deletion indicator.
'student' becomes 'L' (learner, as in L-plates for learner drivers).
'sleek' with 'l' taken away is 'SEEK'.
(Other definitions for seek that I've seen before include "'. . . . and ye shall find'" , "Attempt to find; ask for" , "Ask for (permission)" , "Attempt - search" , "Hunt, look for" .)