Difficult problem? Student's lost heart (6)
I believe the answer is:
ticker
'heart' is the definition.
(synonyms)
'difficult problem? student's lost' is the wordplay.
'difficult problem?' becomes 'tickler' (I've seen this before).
'student' becomes 'l' (as in L-plates for learner drivers).
'lost' is a deletion indicator.
'tickler' with 'l' removed is 'TICKER'.
(Other definitions for ticker that I've seen before include "timer" , "Heart like a clock" , "Telegraph instrument" , "Old clock or slang heart (6)" , "Old watch or informal heart" .)