Initially rush around in dawn attack (4)
I believe the answer is:
raid
'attack' is the definition.
(I know that raid is a type of incursion)
'initially rush around in dawn' is the wordplay.
'initially' indicates taking the first letters.
The initial letters of 'rush around in dawn' is 'RAID'.
(Other definitions for raid that I've seen before include "Foray, sudden attack" , "Smash-and-grab?" , "Enter a territory and take spoils" , "Surprise police visit" , "Maraud" .)