Staff officer, pushy, busy with collaring squadron leader (5,3)
I believe the answer is:
brass hat
'staff officer' is the definition.
(brass hat can informally mean a military officer)
'pushy busy with collaring squadron leader' is the wordplay.
'pushy' becomes 'brash' (I've seen this before).
'busy with' becomes 'at' (I've seen this in other clues).
'collaring' is an insertion indicator.
'leader' indicates taking the first letters.
The first letter of 'squadron' is 's'.
'brash'+'at'='brashat'
'brashat' enclosing 's' is 'BRASS HAT'.
(Other definitions for brass hat that I've seen before include "Certainly no private" , "official of the first rank" , "Senior mil. officer (slang)" , "Top-ranking officer" , "High-ranking military officer" .)