Longing to head off to the ground (4)
I believe the answer is:
itch
'longing' is the definition.
(I've seen this before)
'head off to the ground' is the wordplay.
'head off' means to remove the first letter.
'to the ground' becomes 'pitch' (I've seen this before).
'pitch' with its first letter taken away is 'ITCH'.
'to' is the link.
(Other definitions for itch that I've seen before include "Yen" , "Feel tingling sensation in skin" , "Hankering" , "It must be scratched" , "Prickling" .)