Difficult problem? Learner's lost heart (6)
I believe the answer is:
ticker
'heart' is the definition.
(synonyms)
'difficult problem? learner's lost' is the wordplay.
'difficult problem?' becomes 'stickler' (I've seen this in another clue).
'learner's' becomes 'l's' (as in a learner driver with L-plates on their car).
'lost' indicates named letters should be taken away.
'stickler' with 'ls' taken away is 'TICKER'.
(Other definitions for ticker that I've seen before include "- - -tape machine" , "Old watch or informal heart" , "teacher giving correct marks" , "Heart (sl.)" , "Old clock or slang heart (6)" .)