Search for hard nut to crack (4)
I believe the answer is:
hunt
'search for' is the definition.
(I've seen this in another clue)
'hard nut to crack' is the wordplay.
'hard' becomes 'h' (abbreviation used in pencil classifications).
'to crack' indicates an anagram (I've seen 'cracking' mean this).
'nut' anagrammed gives 'unt'.
'h'+'unt'='HUNT'
(Other definitions for hunt that I've seen before include "Pursue quarry" , "Search (with dogs?)" , "Search; chase" , "Pursue game" , "Pursue (animal) for food or sport" .)