Difficult journey (4)
(Other definitions for slog that I've seen before include "Very tiring work" , "Hit out without style" , "Work doggedly" , "Hit hard - hard work" , "Work (or walk) involving great effort" .)
'difficult journey' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for trek that I've seen before include "Long walk in the mountains?" , "Slog" , "Footslog" , "Expedition or difficult trip" , "A long arduous journey as in S Africa" .)