Long hold-up heading off (4)
I believe the answer is:
itch
'long' is the definition.
(to long or itch for something is to desire it)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for itch that I've seen before include "Impatient desire (colloq.)" , "Yen" , "It must be scratched" , "minor irritant" , "Long" .)