Scratching head, supply joke (4)
I believe the answer is:
quip
'joke' is the definition.
(a quip is a joke or witticism)
'scratching head supply' is the wordplay.
'scratching head' means to remove the first letter (the first letter or head is scratched out).
'supply' becomes 'equip' (equipping is a kind of supplying).
'equip' with its first letter taken off is 'QUIP'.
(Other definitions for quip that I've seen before include "Bon mot" , "Wisecrack" , "West African country" , "Verbal sally" , "Brief witty saying" .)